id	sid	tid	token	lemma	pos
american_scientific_journal-7486	1	1	77	77	NUM
american_scientific_journal-7486	1	2	american	american	ADJ
american_scientific_journal-7486	1	3	academic	academic	ADJ
american_scientific_journal-7486	1	4	scientific	scientific	ADJ
american_scientific_journal-7486	1	5	research	research	NOUN
american_scientific_journal-7486	1	6	journal	journal	NOUN
american_scientific_journal-7486	1	7	for	for	ADP
american_scientific_journal-7486	1	8	engineering	engineering	NOUN
american_scientific_journal-7486	1	9	,	,	PUNCT
american_scientific_journal-7486	1	10	technology	technology	NOUN
american_scientific_journal-7486	1	11	,	,	PUNCT
american_scientific_journal-7486	1	12	and	and	CCONJ
american_scientific_journal-7486	1	13	sciences	sciences	PROPN
american_scientific_journal-7486	1	14	issn	issn	PROPN
american_scientific_journal-7486	1	15	(	(	PUNCT
american_scientific_journal-7486	1	16	print	print	NOUN
american_scientific_journal-7486	1	17	)	)	PUNCT
american_scientific_journal-7486	1	18	2313	2313	NUM
american_scientific_journal-7486	1	19	-	-	SYM
american_scientific_journal-7486	1	20	4410	4410	NUM
american_scientific_journal-7486	1	21	,	,	PUNCT
american_scientific_journal-7486	1	22	issn	issn	PROPN
american_scientific_journal-7486	1	23	(	(	PUNCT
american_scientific_journal-7486	1	24	online	online	ADJ
american_scientific_journal-7486	1	25	)	)	PUNCT
american_scientific_journal-7486	1	26	2313	2313	NUM
american_scientific_journal-7486	1	27	-	-	SYM
american_scientific_journal-7486	1	28	4402	4402	NUM
american_scientific_journal-7486	1	29	http://asrjetsjournal.org/	http://asrjetsjournal.org/	NOUN
american_scientific_journal-7486	1	30	a	a	DET
american_scientific_journal-7486	1	31	new	new	ADJ
american_scientific_journal-7486	1	32	approach	approach	NOUN
american_scientific_journal-7486	1	33	for	for	ADP
american_scientific_journal-7486	1	34	examining	examine	VERB
american_scientific_journal-7486	1	35	a	a	DET
american_scientific_journal-7486	1	36	given	give	VERB
american_scientific_journal-7486	1	37	number	number	NOUN
american_scientific_journal-7486	1	38	to	to	PART
american_scientific_journal-7486	1	39	be	be	AUX
american_scientific_journal-7486	1	40	a	a	DET
american_scientific_journal-7486	1	41	prime	prime	ADJ
american_scientific_journal-7486	1	42	number	number	NOUN
american_scientific_journal-7486	1	43	lourens	louren	VERB
american_scientific_journal-7486	1	44	nicolaas	nicolaas	ADJ
american_scientific_journal-7486	1	45	jacobus	jacobus	PROPN
american_scientific_journal-7486	1	46	engelbrecht	engelbrecht	PROPN
american_scientific_journal-7486	1	47	*	*	PUNCT
american_scientific_journal-7486	1	48	independent	independent	ADJ
american_scientific_journal-7486	1	49	researcher	researcher	NOUN
american_scientific_journal-7486	1	50	,	,	PUNCT
american_scientific_journal-7486	1	51	33	33	NUM
american_scientific_journal-7486	1	52	william	william	PROPN
american_scientific_journal-7486	1	53	road	road	PROPN
american_scientific_journal-7486	1	54	,	,	PUNCT
american_scientific_journal-7486	1	55	pringle	pringle	PROPN
american_scientific_journal-7486	1	56	bay	bay	PROPN
american_scientific_journal-7486	1	57	,	,	PUNCT
american_scientific_journal-7486	1	58	7196	7196	NUM
american_scientific_journal-7486	1	59	,	,	PUNCT
american_scientific_journal-7486	1	60	south	south	PROPN
american_scientific_journal-7486	1	61	africa	africa	PROPN
american_scientific_journal-7486	1	62	email	email	NOUN
american_scientific_journal-7486	1	63	:	:	PUNCT
american_scientific_journal-7486	1	64	engelbrechtlourie@gmail.com	engelbrechtlourie@gmail.com	PROPN
american_scientific_journal-7486	2	1	abstract	abstract	ADJ
american_scientific_journal-7486	2	2	any	any	DET
american_scientific_journal-7486	2	3	whole	whole	ADJ
american_scientific_journal-7486	2	4	number	number	NOUN
american_scientific_journal-7486	2	5	greater	great	ADJ
american_scientific_journal-7486	2	6	than	than	ADP
american_scientific_journal-7486	2	7	1	1	NUM
american_scientific_journal-7486	2	8	that	that	PRON
american_scientific_journal-7486	2	9	is	be	AUX
american_scientific_journal-7486	2	10	divisible	divisible	ADJ
american_scientific_journal-7486	2	11	only	only	ADV
american_scientific_journal-7486	2	12	by	by	ADP
american_scientific_journal-7486	2	13	1	1	NUM
american_scientific_journal-7486	2	14	and	and	CCONJ
american_scientific_journal-7486	2	15	itself	itself	PRON
american_scientific_journal-7486	2	16	,	,	PUNCT
american_scientific_journal-7486	2	17	is	be	AUX
american_scientific_journal-7486	2	18	defined	define	VERB
american_scientific_journal-7486	2	19	as	as	ADP
american_scientific_journal-7486	2	20	a	a	DET
american_scientific_journal-7486	2	21	prime	prime	ADJ
american_scientific_journal-7486	2	22	number	number	NOUN
american_scientific_journal-7486	2	23	.	.	PUNCT
american_scientific_journal-7486	3	1	therefore	therefore	ADV
american_scientific_journal-7486	3	2	a	a	DET
american_scientific_journal-7486	3	3	prime	prime	NOUN
american_scientific_journal-7486	3	4	is	be	AUX
american_scientific_journal-7486	3	5	a	a	DET
american_scientific_journal-7486	3	6	number	number	NOUN
american_scientific_journal-7486	3	7	that	that	PRON
american_scientific_journal-7486	3	8	has	have	VERB
american_scientific_journal-7486	3	9	only	only	ADV
american_scientific_journal-7486	3	10	two	two	NUM
american_scientific_journal-7486	3	11	factors	factor	NOUN
american_scientific_journal-7486	3	12	.	.	PUNCT
american_scientific_journal-7486	4	1	the	the	DET
american_scientific_journal-7486	4	2	chaotic	chaotic	ADJ
american_scientific_journal-7486	4	3	nature	nature	NOUN
american_scientific_journal-7486	4	4	of	of	ADP
american_scientific_journal-7486	4	5	prime	prime	ADJ
american_scientific_journal-7486	4	6	numbers	number	NOUN
american_scientific_journal-7486	4	7	in	in	ADP
american_scientific_journal-7486	4	8	the	the	DET
american_scientific_journal-7486	4	9	set	set	NOUN
american_scientific_journal-7486	4	10	of	of	ADP
american_scientific_journal-7486	4	11	integer	integer	NOUN
american_scientific_journal-7486	4	12	numbers	number	NOUN
american_scientific_journal-7486	4	13	makes	make	VERB
american_scientific_journal-7486	4	14	it	it	PRON
american_scientific_journal-7486	4	15	important	important	ADJ
american_scientific_journal-7486	4	16	in	in	ADP
american_scientific_journal-7486	4	17	today	today	NOUN
american_scientific_journal-7486	4	18	’s	’s	PART
american_scientific_journal-7486	4	19	world	world	NOUN
american_scientific_journal-7486	4	20	,	,	PUNCT
american_scientific_journal-7486	4	21	particularly	particularly	ADV
american_scientific_journal-7486	4	22	in	in	ADP
american_scientific_journal-7486	4	23	cryptosystems	cryptosystem	NOUN
american_scientific_journal-7486	4	24	.	.	PUNCT
american_scientific_journal-7486	5	1	if	if	SCONJ
american_scientific_journal-7486	5	2	it	it	PRON
american_scientific_journal-7486	5	3	was	be	AUX
american_scientific_journal-7486	5	4	possible	possible	ADJ
american_scientific_journal-7486	5	5	to	to	PART
american_scientific_journal-7486	5	6	determine	determine	VERB
american_scientific_journal-7486	5	7	the	the	DET
american_scientific_journal-7486	5	8	predictable	predictable	ADJ
american_scientific_journal-7486	5	9	nature	nature	NOUN
american_scientific_journal-7486	5	10	of	of	ADP
american_scientific_journal-7486	5	11	primes	prime	NOUN
american_scientific_journal-7486	5	12	,	,	PUNCT
american_scientific_journal-7486	5	13	the	the	DET
american_scientific_journal-7486	5	14	cryptosystems	cryptosystem	NOUN
american_scientific_journal-7486	5	15	of	of	ADP
american_scientific_journal-7486	5	16	the	the	DET
american_scientific_journal-7486	5	17	world	world	NOUN
american_scientific_journal-7486	5	18	could	could	AUX
american_scientific_journal-7486	5	19	crash	crash	VERB
american_scientific_journal-7486	5	20	.	.	PUNCT
american_scientific_journal-7486	6	1	there	there	PRON
american_scientific_journal-7486	6	2	are	be	VERB
american_scientific_journal-7486	6	3	a	a	DET
american_scientific_journal-7486	6	4	number	number	NOUN
american_scientific_journal-7486	6	5	of	of	ADP
american_scientific_journal-7486	6	6	mathematical	mathematical	ADJ
american_scientific_journal-7486	6	7	arguments	argument	NOUN
american_scientific_journal-7486	6	8	backing	back	VERB
american_scientific_journal-7486	6	9	the	the	DET
american_scientific_journal-7486	6	10	fact	fact	NOUN
american_scientific_journal-7486	6	11	that	that	SCONJ
american_scientific_journal-7486	6	12	it	it	PRON
american_scientific_journal-7486	6	13	is	be	AUX
american_scientific_journal-7486	6	14	not	not	PART
american_scientific_journal-7486	6	15	possible	possible	ADJ
american_scientific_journal-7486	6	16	to	to	PART
american_scientific_journal-7486	6	17	predict	predict	VERB
american_scientific_journal-7486	6	18	the	the	DET
american_scientific_journal-7486	6	19	nature	nature	NOUN
american_scientific_journal-7486	6	20	of	of	ADP
american_scientific_journal-7486	6	21	prime	prime	ADJ
american_scientific_journal-7486	6	22	numbers	number	NOUN
american_scientific_journal-7486	6	23	.	.	PUNCT
american_scientific_journal-7486	7	1	so	so	ADV
american_scientific_journal-7486	7	2	one	one	PRON
american_scientific_journal-7486	7	3	can	can	AUX
american_scientific_journal-7486	7	4	only	only	ADV
american_scientific_journal-7486	7	5	formulate	formulate	VERB
american_scientific_journal-7486	7	6	a	a	DET
american_scientific_journal-7486	7	7	tool	tool	NOUN
american_scientific_journal-7486	7	8	for	for	ADP
american_scientific_journal-7486	7	9	testing	test	VERB
american_scientific_journal-7486	7	10	whether	whether	SCONJ
american_scientific_journal-7486	7	11	a	a	DET
american_scientific_journal-7486	7	12	given	give	VERB
american_scientific_journal-7486	7	13	number	number	NOUN
american_scientific_journal-7486	7	14	is	be	AUX
american_scientific_journal-7486	7	15	likely	likely	ADJ
american_scientific_journal-7486	7	16	to	to	PART
american_scientific_journal-7486	7	17	be	be	AUX
american_scientific_journal-7486	7	18	a	a	DET
american_scientific_journal-7486	7	19	prime	prime	ADJ
american_scientific_journal-7486	7	20	number	number	NOUN
american_scientific_journal-7486	7	21	.	.	PUNCT
american_scientific_journal-7486	8	1	following	follow	VERB
american_scientific_journal-7486	8	2	the	the	DET
american_scientific_journal-7486	8	3	theme	theme	NOUN
american_scientific_journal-7486	8	4	,	,	PUNCT
american_scientific_journal-7486	8	5	here	here	ADV
american_scientific_journal-7486	8	6	in	in	ADP
american_scientific_journal-7486	8	7	this	this	DET
american_scientific_journal-7486	8	8	article	article	NOUN
american_scientific_journal-7486	8	9	,	,	PUNCT
american_scientific_journal-7486	8	10	we	we	PRON
american_scientific_journal-7486	8	11	also	also	ADV
american_scientific_journal-7486	8	12	formulate	formulate	VERB
american_scientific_journal-7486	8	13	a	a	DET
american_scientific_journal-7486	8	14	method	method	NOUN
american_scientific_journal-7486	8	15	to	to	PART
american_scientific_journal-7486	8	16	check	check	VERB
american_scientific_journal-7486	8	17	whether	whether	SCONJ
american_scientific_journal-7486	8	18	a	a	DET
american_scientific_journal-7486	8	19	given	give	VERB
american_scientific_journal-7486	8	20	number	number	NOUN
american_scientific_journal-7486	8	21	is	be	AUX
american_scientific_journal-7486	8	22	a	a	DET
american_scientific_journal-7486	8	23	probable	probable	ADJ
american_scientific_journal-7486	8	24	prime	prime	ADJ
american_scientific_journal-7486	8	25	number	number	NOUN
american_scientific_journal-7486	8	26	or	or	CCONJ
american_scientific_journal-7486	8	27	not	not	PART
american_scientific_journal-7486	8	28	.	.	PUNCT
american_scientific_journal-7486	9	1	we	we	PRON
american_scientific_journal-7486	9	2	also	also	ADV
american_scientific_journal-7486	9	3	derive	derive	VERB
american_scientific_journal-7486	9	4	a	a	DET
american_scientific_journal-7486	9	5	connection	connection	NOUN
american_scientific_journal-7486	9	6	between	between	ADP
american_scientific_journal-7486	9	7	the	the	DET
american_scientific_journal-7486	9	8	collatz	collatz	NOUN
american_scientific_journal-7486	9	9	conjecture	conjecture	NOUN
american_scientific_journal-7486	9	10	and	and	CCONJ
american_scientific_journal-7486	9	11	prime	prime	ADJ
american_scientific_journal-7486	9	12	numbers	number	NOUN
american_scientific_journal-7486	9	13	.	.	PUNCT
american_scientific_journal-7486	10	1	keywords	keyword	NOUN
american_scientific_journal-7486	10	2	:	:	PUNCT
american_scientific_journal-7486	10	3	congruence	congruence	PROPN
american_scientific_journal-7486	10	4	;	;	PUNCT
american_scientific_journal-7486	10	5	collatz	collatz	NOUN
american_scientific_journal-7486	10	6	conjecture	conjecture	NOUN
american_scientific_journal-7486	10	7	;	;	PUNCT
american_scientific_journal-7486	10	8	matlab	matlab	PROPN
american_scientific_journal-7486	10	9	programming	programming	NOUN
american_scientific_journal-7486	10	10	;	;	PUNCT
american_scientific_journal-7486	10	11	prime	prime	ADJ
american_scientific_journal-7486	10	12	numbers	number	NOUN
american_scientific_journal-7486	10	13	;	;	PUNCT
american_scientific_journal-7486	10	14	primality	primality	NOUN
american_scientific_journal-7486	10	15	test	test	NOUN
american_scientific_journal-7486	10	16	.	.	PUNCT
american_scientific_journal-7486	11	1	1	1	X
american_scientific_journal-7486	11	2	.	.	X
american_scientific_journal-7486	11	3	introduction	introduction	NOUN
american_scientific_journal-7486	11	4	mathematical	mathematical	ADJ
american_scientific_journal-7486	11	5	theorems	theorem	NOUN
american_scientific_journal-7486	11	6	are	be	AUX
american_scientific_journal-7486	11	7	important	important	ADJ
american_scientific_journal-7486	11	8	building	building	NOUN
american_scientific_journal-7486	11	9	blocks	block	NOUN
american_scientific_journal-7486	11	10	for	for	ADP
american_scientific_journal-7486	11	11	mathematics	mathematics	NOUN
american_scientific_journal-7486	11	12	and	and	CCONJ
american_scientific_journal-7486	11	13	computing	computing	NOUN
american_scientific_journal-7486	11	14	.	.	PUNCT
american_scientific_journal-7486	12	1	the	the	DET
american_scientific_journal-7486	12	2	theory	theory	NOUN
american_scientific_journal-7486	12	3	of	of	ADP
american_scientific_journal-7486	12	4	prime	prime	ADJ
american_scientific_journal-7486	12	5	numbers	number	NOUN
american_scientific_journal-7486	12	6	and	and	CCONJ
american_scientific_journal-7486	12	7	the	the	DET
american_scientific_journal-7486	12	8	theorems	theorem	NOUN
american_scientific_journal-7486	12	9	related	relate	VERB
american_scientific_journal-7486	12	10	to	to	ADP
american_scientific_journal-7486	12	11	prime	prime	ADJ
american_scientific_journal-7486	12	12	numbers	number	NOUN
american_scientific_journal-7486	12	13	are	be	AUX
american_scientific_journal-7486	12	14	widely	widely	ADV
american_scientific_journal-7486	12	15	used	use	VERB
american_scientific_journal-7486	12	16	in	in	ADP
american_scientific_journal-7486	12	17	information	information	NOUN
american_scientific_journal-7486	12	18	technology	technology	NOUN
american_scientific_journal-7486	12	19	such	such	ADJ
american_scientific_journal-7486	12	20	as	as	ADP
american_scientific_journal-7486	12	21	publickey	publickey	ADJ
american_scientific_journal-7486	12	22	cryptography	cryptography	NOUN
american_scientific_journal-7486	12	23	.	.	PUNCT
american_scientific_journal-7486	13	1	although	although	SCONJ
american_scientific_journal-7486	13	2	no	no	DET
american_scientific_journal-7486	13	3	general	general	ADJ
american_scientific_journal-7486	13	4	formula	formula	NOUN
american_scientific_journal-7486	13	5	for	for	ADP
american_scientific_journal-7486	13	6	prime	prime	ADJ
american_scientific_journal-7486	13	7	numbers	number	NOUN
american_scientific_journal-7486	13	8	exist	exist	VERB
american_scientific_journal-7486	13	9	yet	yet	ADV
american_scientific_journal-7486	13	10	,	,	PUNCT
american_scientific_journal-7486	13	11	the	the	DET
american_scientific_journal-7486	13	12	search	search	NOUN
american_scientific_journal-7486	13	13	for	for	ADP
american_scientific_journal-7486	13	14	a	a	DET
american_scientific_journal-7486	13	15	more	more	ADV
american_scientific_journal-7486	13	16	efficient	efficient	ADJ
american_scientific_journal-7486	13	17	or	or	CCONJ
american_scientific_journal-7486	13	18	parallel	parallel	ADJ
american_scientific_journal-7486	13	19	formula	formula	NOUN
american_scientific_journal-7486	13	20	for	for	ADP
american_scientific_journal-7486	13	21	finding	find	VERB
american_scientific_journal-7486	13	22	probable	probable	ADJ
american_scientific_journal-7486	13	23	prime	prime	ADJ
american_scientific_journal-7486	13	24	numbers	number	NOUN
american_scientific_journal-7486	13	25	are	be	AUX
american_scientific_journal-7486	13	26	of	of	ADP
american_scientific_journal-7486	13	27	the	the	DET
american_scientific_journal-7486	13	28	utmost	utmost	ADJ
american_scientific_journal-7486	13	29	importance	importance	NOUN
american_scientific_journal-7486	13	30	as	as	SCONJ
american_scientific_journal-7486	13	31	to	to	PART
american_scientific_journal-7486	13	32	save	save	VERB
american_scientific_journal-7486	13	33	time	time	NOUN
american_scientific_journal-7486	13	34	on	on	ADP
american_scientific_journal-7486	13	35	irrelevant	irrelevant	ADJ
american_scientific_journal-7486	13	36	possibilities	possibility	NOUN
american_scientific_journal-7486	13	37	such	such	ADJ
american_scientific_journal-7486	13	38	as	as	ADP
american_scientific_journal-7486	13	39	composite	composite	ADJ
american_scientific_journal-7486	13	40	numbers	number	NOUN
american_scientific_journal-7486	13	41	.	.	PUNCT
american_scientific_journal-7486	14	1	a	a	DET
american_scientific_journal-7486	14	2	primality	primality	NOUN
american_scientific_journal-7486	14	3	test	test	NOUN
american_scientific_journal-7486	14	4	is	be	AUX
american_scientific_journal-7486	14	5	an	an	DET
american_scientific_journal-7486	14	6	algorithm	algorithm	NOUN
american_scientific_journal-7486	14	7	for	for	ADP
american_scientific_journal-7486	14	8	determining	determine	VERB
american_scientific_journal-7486	14	9	whether	whether	SCONJ
american_scientific_journal-7486	14	10	an	an	DET
american_scientific_journal-7486	14	11	input	input	NOUN
american_scientific_journal-7486	14	12	number	number	NOUN
american_scientific_journal-7486	14	13	is	be	AUX
american_scientific_journal-7486	14	14	a	a	DET
american_scientific_journal-7486	14	15	prbable	prbable	ADJ
american_scientific_journal-7486	14	16	prime	prime	NOUN
american_scientific_journal-7486	14	17	or	or	CCONJ
american_scientific_journal-7486	14	18	not	not	PART
american_scientific_journal-7486	14	19	.	.	PUNCT
american_scientific_journal-7486	15	1	primality	primality	NOUN
american_scientific_journal-7486	15	2	tests	test	VERB
american_scientific_journal-7486	15	3	only	only	ADV
american_scientific_journal-7486	15	4	state	state	VERB
american_scientific_journal-7486	15	5	whether	whether	SCONJ
american_scientific_journal-7486	15	6	the	the	DET
american_scientific_journal-7486	15	7	input	input	NOUN
american_scientific_journal-7486	15	8	number	number	NOUN
american_scientific_journal-7486	15	9	is	be	AUX
american_scientific_journal-7486	15	10	likely	likely	ADJ
american_scientific_journal-7486	15	11	to	to	PART
american_scientific_journal-7486	15	12	be	be	AUX
american_scientific_journal-7486	15	13	prime	prime	ADJ
american_scientific_journal-7486	15	14	or	or	CCONJ
american_scientific_journal-7486	15	15	not	not	PART
american_scientific_journal-7486	15	16	.	.	PUNCT
american_scientific_journal-7486	16	1	a	a	DET
american_scientific_journal-7486	16	2	few	few	ADJ
american_scientific_journal-7486	16	3	mathematical	mathematical	ADJ
american_scientific_journal-7486	16	4	formulas	formula	NOUN
american_scientific_journal-7486	16	5	for	for	ADP
american_scientific_journal-7486	16	6	identifying	identify	VERB
american_scientific_journal-7486	16	7	probable	probable	ADJ
american_scientific_journal-7486	16	8	primes	prime	NOUN
american_scientific_journal-7486	16	9	do	do	AUX
american_scientific_journal-7486	16	10	exist	exist	VERB
american_scientific_journal-7486	16	11	and	and	CCONJ
american_scientific_journal-7486	16	12	are	be	AUX
american_scientific_journal-7486	16	13	translated	translate	VERB
american_scientific_journal-7486	16	14	into	into	ADP
american_scientific_journal-7486	16	15	computer	computer	NOUN
american_scientific_journal-7486	16	16	codes	code	NOUN
american_scientific_journal-7486	16	17	such	such	ADJ
american_scientific_journal-7486	16	18	as	as	ADP
american_scientific_journal-7486	16	19	python	python	NOUN
american_scientific_journal-7486	16	20	,	,	PUNCT
american_scientific_journal-7486	16	21	c++	c++	NOUN
american_scientific_journal-7486	16	22	,	,	PUNCT
american_scientific_journal-7486	16	23	java	java	PROPN
american_scientific_journal-7486	16	24	script	script	NOUN
american_scientific_journal-7486	16	25	and	and	CCONJ
american_scientific_journal-7486	16	26	r	r	NOUN
american_scientific_journal-7486	16	27	which	which	PRON
american_scientific_journal-7486	16	28	execute	execute	VERB
american_scientific_journal-7486	16	29	the	the	DET
american_scientific_journal-7486	16	30	primality	primality	NOUN
american_scientific_journal-7486	16	31	testing	testing	NOUN
american_scientific_journal-7486	16	32	.	.	PUNCT
american_scientific_journal-7486	17	1	one	one	NUM
american_scientific_journal-7486	17	2	of	of	ADP
american_scientific_journal-7486	17	3	the	the	DET
american_scientific_journal-7486	17	4	examples	example	NOUN
american_scientific_journal-7486	17	5	of	of	ADP
american_scientific_journal-7486	17	6	the	the	DET
american_scientific_journal-7486	17	7	primality	primality	NOUN
american_scientific_journal-7486	17	8	tests	test	NOUN
american_scientific_journal-7486	17	9	is	be	AUX
american_scientific_journal-7486	17	10	fermat	fermat	PROPN
american_scientific_journal-7486	17	11	’s	’s	PART
american_scientific_journal-7486	17	12	primality	primality	NOUN
american_scientific_journal-7486	17	13	test	test	NOUN
american_scientific_journal-7486	17	14	.	.	PUNCT
american_scientific_journal-7486	18	1	in	in	ADP
american_scientific_journal-7486	18	2	this	this	DET
american_scientific_journal-7486	18	3	test	test	NOUN
american_scientific_journal-7486	18	4	,	,	PUNCT
american_scientific_journal-7486	18	5	fermat	fermat	PROPN
american_scientific_journal-7486	18	6	’s	’s	PART
american_scientific_journal-7486	18	7	theorem	theorem	ADJ
american_scientific_journal-7486	18	8	and	and	CCONJ
american_scientific_journal-7486	18	9	modular	modular	ADJ
american_scientific_journal-7486	18	10	exponentiation	exponentiation	NOUN
american_scientific_journal-7486	18	11	is	be	AUX
american_scientific_journal-7486	18	12	used	use	VERB
american_scientific_journal-7486	18	13	to	to	PART
american_scientific_journal-7486	18	14	give	give	VERB
american_scientific_journal-7486	18	15	a	a	DET
american_scientific_journal-7486	18	16	way	way	NOUN
american_scientific_journal-7486	18	17	to	to	PART
american_scientific_journal-7486	18	18	test	test	VERB
american_scientific_journal-7486	18	19	if	if	SCONJ
american_scientific_journal-7486	18	20	a	a	DET
american_scientific_journal-7486	18	21	number	number	NOUN
american_scientific_journal-7486	18	22	is	be	AUX
american_scientific_journal-7486	18	23	a	a	DET
american_scientific_journal-7486	18	24	probable	probable	ADJ
american_scientific_journal-7486	18	25	prime	prime	ADJ
american_scientific_journal-7486	18	26	number	number	NOUN
american_scientific_journal-7486	18	27	,	,	PUNCT
american_scientific_journal-7486	18	28	(	(	PUNCT
american_scientific_journal-7486	18	29	for	for	ADP
american_scientific_journal-7486	18	30	more	more	ADJ
american_scientific_journal-7486	18	31	see	see	NOUN
american_scientific_journal-7486	18	32	[	[	X
american_scientific_journal-7486	18	33	1	1	NUM
american_scientific_journal-7486	18	34	]	]	NUM
american_scientific_journal-7486	18	35	)	)	PUNCT
american_scientific_journal-7486	18	36	.	.	PUNCT
american_scientific_journal-7486	19	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-7486	20	1	*	*	PUNCT
american_scientific_journal-7486	20	2	corresponding	correspond	VERB
american_scientific_journal-7486	20	3	author	author	NOUN
american_scientific_journal-7486	20	4	.	.	PUNCT
american_scientific_journal-7486	21	1	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PRON
american_scientific_journal-7486	21	2	https://www.cuemath.com/numbers/prime-numbers/	https://www.cuemath.com/numbers/prime-numbers/	PROPN
american_scientific_journal-7486	21	3	american	american	ADJ
american_scientific_journal-7486	21	4	academic	academic	ADJ
american_scientific_journal-7486	21	5	scientific	scientific	ADJ
american_scientific_journal-7486	21	6	research	research	NOUN
american_scientific_journal-7486	21	7	journal	journal	NOUN
american_scientific_journal-7486	21	8	for	for	ADP
american_scientific_journal-7486	21	9	engineering	engineering	NOUN
american_scientific_journal-7486	21	10	,	,	PUNCT
american_scientific_journal-7486	21	11	technology	technology	NOUN
american_scientific_journal-7486	21	12	,	,	PUNCT
american_scientific_journal-7486	21	13	and	and	CCONJ
american_scientific_journal-7486	21	14	sciences	science	NOUN
american_scientific_journal-7486	21	15	(	(	PUNCT
american_scientific_journal-7486	21	16	asrjets	asrjet	NOUN
american_scientific_journal-7486	21	17	)	)	PUNCT
american_scientific_journal-7486	21	18	(	(	PUNCT
american_scientific_journal-7486	21	19	2022	2022	NUM
american_scientific_journal-7486	21	20	)	)	PUNCT
american_scientific_journal-7486	21	21	volume	volume	NOUN
american_scientific_journal-7486	21	22	88	88	NUM
american_scientific_journal-7486	21	23	,	,	PUNCT
american_scientific_journal-7486	21	24	no	no	DET
american_scientific_journal-7486	21	25	1	1	NUM
american_scientific_journal-7486	21	26	,	,	PUNCT
american_scientific_journal-7486	21	27	pp	pp	ADV
american_scientific_journal-7486	21	28	77	77	NUM
american_scientific_journal-7486	21	29	-	-	SYM
american_scientific_journal-7486	21	30	90	90	NUM
american_scientific_journal-7486	21	31	78	78	NUM
american_scientific_journal-7486	21	32	similarly	similarly	ADV
american_scientific_journal-7486	21	33	,	,	PUNCT
american_scientific_journal-7486	21	34	rabin	rabin	PROPN
american_scientific_journal-7486	21	35	–	–	PUNCT
american_scientific_journal-7486	21	36	miller	miller	PROPN
american_scientific_journal-7486	21	37	’s	’s	PART
american_scientific_journal-7486	21	38	primality	primality	NOUN
american_scientific_journal-7486	21	39	test	test	NOUN
american_scientific_journal-7486	21	40	is	be	AUX
american_scientific_journal-7486	21	41	a	a	DET
american_scientific_journal-7486	21	42	test	test	NOUN
american_scientific_journal-7486	21	43	using	use	VERB
american_scientific_journal-7486	21	44	probabilistic	probabilistic	ADJ
american_scientific_journal-7486	21	45	methods	method	NOUN
american_scientific_journal-7486	21	46	.	.	PUNCT
american_scientific_journal-7486	22	1	in	in	ADP
american_scientific_journal-7486	22	2	this	this	DET
american_scientific_journal-7486	22	3	test	test	NOUN
american_scientific_journal-7486	22	4	,	,	PUNCT
american_scientific_journal-7486	22	5	an	an	DET
american_scientific_journal-7486	22	6	algorithm	algorithm	NOUN
american_scientific_journal-7486	22	7	using	use	VERB
american_scientific_journal-7486	22	8	probability	probability	NOUN
american_scientific_journal-7486	22	9	is	be	AUX
american_scientific_journal-7486	22	10	formulated	formulate	VERB
american_scientific_journal-7486	22	11	which	which	PRON
american_scientific_journal-7486	22	12	says	say	VERB
american_scientific_journal-7486	22	13	whether	whether	SCONJ
american_scientific_journal-7486	22	14	a	a	DET
american_scientific_journal-7486	22	15	given	give	VERB
american_scientific_journal-7486	22	16	number	number	NOUN
american_scientific_journal-7486	22	17	is	be	AUX
american_scientific_journal-7486	22	18	likely	likely	ADJ
american_scientific_journal-7486	22	19	to	to	PART
american_scientific_journal-7486	22	20	be	be	AUX
american_scientific_journal-7486	22	21	prime	prime	ADJ
american_scientific_journal-7486	22	22	,	,	PUNCT
american_scientific_journal-7486	22	23	(	(	PUNCT
american_scientific_journal-7486	22	24	see	see	VERB
american_scientific_journal-7486	22	25	[	[	X
american_scientific_journal-7486	22	26	2	2	NUM
american_scientific_journal-7486	22	27	]	]	NUM
american_scientific_journal-7486	22	28	)	)	PUNCT
american_scientific_journal-7486	22	29	.	.	PUNCT
american_scientific_journal-7486	23	1	another	another	DET
american_scientific_journal-7486	23	2	example	example	NOUN
american_scientific_journal-7486	23	3	of	of	ADP
american_scientific_journal-7486	23	4	a	a	DET
american_scientific_journal-7486	23	5	primality	primality	NOUN
american_scientific_journal-7486	23	6	test	test	NOUN
american_scientific_journal-7486	23	7	using	use	VERB
american_scientific_journal-7486	23	8	probability	probability	NOUN
american_scientific_journal-7486	23	9	is	be	AUX
american_scientific_journal-7486	23	10	the	the	DET
american_scientific_journal-7486	23	11	solovay	solovay	NOUN
american_scientific_journal-7486	23	12	–	–	PUNCT
american_scientific_journal-7486	23	13	strassen	strassen	NOUN
american_scientific_journal-7486	23	14	primality	primality	NOUN
american_scientific_journal-7486	23	15	test	test	NOUN
american_scientific_journal-7486	23	16	,	,	PUNCT
american_scientific_journal-7486	23	17	which	which	PRON
american_scientific_journal-7486	23	18	helps	help	VERB
american_scientific_journal-7486	23	19	to	to	PART
american_scientific_journal-7486	23	20	determine	determine	VERB
american_scientific_journal-7486	23	21	whether	whether	SCONJ
american_scientific_journal-7486	23	22	a	a	DET
american_scientific_journal-7486	23	23	number	number	NOUN
american_scientific_journal-7486	23	24	is	be	AUX
american_scientific_journal-7486	23	25	composite	composite	ADJ
american_scientific_journal-7486	23	26	or	or	CCONJ
american_scientific_journal-7486	23	27	probable	probable	ADJ
american_scientific_journal-7486	23	28	prime	prime	NOUN
american_scientific_journal-7486	23	29	,	,	PUNCT
american_scientific_journal-7486	23	30	(	(	PUNCT
american_scientific_journal-7486	23	31	see	see	VERB
american_scientific_journal-7486	23	32	[	[	X
american_scientific_journal-7486	23	33	3	3	NUM
american_scientific_journal-7486	23	34	]	]	NUM
american_scientific_journal-7486	23	35	)	)	PUNCT
american_scientific_journal-7486	23	36	.	.	PUNCT
american_scientific_journal-7486	24	1	some	some	DET
american_scientific_journal-7486	24	2	other	other	ADJ
american_scientific_journal-7486	24	3	examples	example	NOUN
american_scientific_journal-7486	24	4	of	of	ADP
american_scientific_journal-7486	24	5	the	the	DET
american_scientific_journal-7486	24	6	methods	method	NOUN
american_scientific_journal-7486	24	7	used	use	VERB
american_scientific_journal-7486	24	8	for	for	ADP
american_scientific_journal-7486	24	9	finding	find	VERB
american_scientific_journal-7486	24	10	prime	prime	ADJ
american_scientific_journal-7486	24	11	numbers	number	NOUN
american_scientific_journal-7486	24	12	are	be	AUX
american_scientific_journal-7486	24	13	the	the	DET
american_scientific_journal-7486	24	14	sieve	sieve	NOUN
american_scientific_journal-7486	24	15	of	of	ADP
american_scientific_journal-7486	24	16	eratosthenes	eratosthene	NOUN
american_scientific_journal-7486	24	17	(	(	PUNCT
american_scientific_journal-7486	24	18	250	250	NUM
american_scientific_journal-7486	24	19	bce	bce	NOUN
american_scientific_journal-7486	24	20	)	)	PUNCT
american_scientific_journal-7486	24	21	and	and	CCONJ
american_scientific_journal-7486	24	22	the	the	DET
american_scientific_journal-7486	24	23	sieve	sieve	NOUN
american_scientific_journal-7486	24	24	of	of	ADP
american_scientific_journal-7486	24	25	sundaram	sundaram	PROPN
american_scientific_journal-7486	24	26	(	(	PUNCT
american_scientific_journal-7486	24	27	1934	1934	NUM
american_scientific_journal-7486	24	28	)	)	PUNCT
american_scientific_journal-7486	24	29	.	.	PUNCT
american_scientific_journal-7486	25	1	more	more	ADV
american_scientific_journal-7486	25	2	recent	recent	ADJ
american_scientific_journal-7486	25	3	progress	progress	NOUN
american_scientific_journal-7486	25	4	was	be	AUX
american_scientific_journal-7486	25	5	the	the	DET
american_scientific_journal-7486	25	6	aks	ak	NOUN
american_scientific_journal-7486	25	7	primality	primality	NOUN
american_scientific_journal-7486	25	8	test	test	NOUN
american_scientific_journal-7486	25	9	,	,	PUNCT
american_scientific_journal-7486	25	10	a	a	DET
american_scientific_journal-7486	25	11	deterministic	deterministic	ADJ
american_scientific_journal-7486	25	12	primality	primality	NOUN
american_scientific_journal-7486	25	13	-	-	PUNCT
american_scientific_journal-7486	25	14	proving	prove	VERB
american_scientific_journal-7486	25	15	algorithm	algorithm	NOUN
american_scientific_journal-7486	25	16	created	create	VERB
american_scientific_journal-7486	25	17	and	and	CCONJ
american_scientific_journal-7486	25	18	published	publish	VERB
american_scientific_journal-7486	25	19	by	by	ADP
american_scientific_journal-7486	25	20	computer	computer	NOUN
american_scientific_journal-7486	25	21	scientists	scientist	NOUN
american_scientific_journal-7486	25	22	agrawal	agrawal	PROPN
american_scientific_journal-7486	25	23	m	m	PROPN
american_scientific_journal-7486	25	24	,	,	PUNCT
american_scientific_journal-7486	25	25	kayal	kayal	PROPN
american_scientific_journal-7486	25	26	m	m	PROPN
american_scientific_journal-7486	25	27	,	,	PUNCT
american_scientific_journal-7486	25	28	and	and	CCONJ
american_scientific_journal-7486	25	29	saxena	saxena	PROPN
american_scientific_journal-7486	25	30	n	n	CCONJ
american_scientific_journal-7486	25	31	,	,	PUNCT
american_scientific_journal-7486	25	32	on	on	ADP
american_scientific_journal-7486	25	33	august	august	PROPN
american_scientific_journal-7486	25	34	6	6	NUM
american_scientific_journal-7486	25	35	,	,	PUNCT
american_scientific_journal-7486	25	36	2002	2002	NUM
american_scientific_journal-7486	25	37	,	,	PUNCT
american_scientific_journal-7486	25	38	in	in	ADP
american_scientific_journal-7486	25	39	an	an	DET
american_scientific_journal-7486	25	40	article	article	NOUN
american_scientific_journal-7486	25	41	titled	title	VERB
american_scientific_journal-7486	25	42	"	"	PUNCT
american_scientific_journal-7486	25	43	primes	prime	NOUN
american_scientific_journal-7486	25	44	is	be	AUX
american_scientific_journal-7486	25	45	in	in	ADP
american_scientific_journal-7486	25	46	p	p	X
american_scientific_journal-7486	25	47	"	"	PUNCT
american_scientific_journal-7486	25	48	.	.	PUNCT
american_scientific_journal-7486	26	1	(	(	PUNCT
american_scientific_journal-7486	26	2	also	also	ADV
american_scientific_journal-7486	26	3	known	know	VERB
american_scientific_journal-7486	26	4	as	as	ADP
american_scientific_journal-7486	26	5	the	the	DET
american_scientific_journal-7486	26	6	agrawal	agrawal	PROPN
american_scientific_journal-7486	26	7	–	–	PUNCT
american_scientific_journal-7486	26	8	kayal	kayal	PROPN
american_scientific_journal-7486	26	9	–	–	PUNCT
american_scientific_journal-7486	26	10	saxena	saxena	PROPN
american_scientific_journal-7486	26	11	primality	primality	PROPN
american_scientific_journal-7486	26	12	test	test	NOUN
american_scientific_journal-7486	26	13	and	and	CCONJ
american_scientific_journal-7486	26	14	cyclotomic	cyclotomic	ADJ
american_scientific_journal-7486	26	15	aks	ak	NOUN
american_scientific_journal-7486	26	16	test	test	NOUN
american_scientific_journal-7486	26	17	)	)	PUNCT
american_scientific_journal-7486	26	18	,	,	PUNCT
american_scientific_journal-7486	26	19	(	(	PUNCT
american_scientific_journal-7486	26	20	see	see	VERB
american_scientific_journal-7486	26	21	[	[	X
american_scientific_journal-7486	26	22	4	4	NUM
american_scientific_journal-7486	26	23	]	]	NUM
american_scientific_journal-7486	26	24	)	)	PUNCT
american_scientific_journal-7486	26	25	.	.	PUNCT
american_scientific_journal-7486	27	1	in	in	ADP
american_scientific_journal-7486	27	2	computational	computational	ADJ
american_scientific_journal-7486	27	3	number	number	NOUN
american_scientific_journal-7486	27	4	theory	theory	NOUN
american_scientific_journal-7486	27	5	,	,	PUNCT
american_scientific_journal-7486	27	6	the	the	DET
american_scientific_journal-7486	27	7	apr	apr	NOUN
american_scientific_journal-7486	27	8	primality	primality	NOUN
american_scientific_journal-7486	27	9	test	test	NOUN
american_scientific_journal-7486	27	10	is	be	AUX
american_scientific_journal-7486	27	11	an	an	DET
american_scientific_journal-7486	27	12	algorithm	algorithm	NOUN
american_scientific_journal-7486	27	13	for	for	ADP
american_scientific_journal-7486	27	14	determining	determine	VERB
american_scientific_journal-7486	27	15	whether	whether	SCONJ
american_scientific_journal-7486	27	16	a	a	DET
american_scientific_journal-7486	27	17	number	number	NOUN
american_scientific_journal-7486	27	18	is	be	AUX
american_scientific_journal-7486	27	19	prime	prime	ADJ
american_scientific_journal-7486	27	20	.	.	PUNCT
american_scientific_journal-7486	28	1	it	it	PRON
american_scientific_journal-7486	28	2	is	be	AUX
american_scientific_journal-7486	28	3	named	name	VERB
american_scientific_journal-7486	28	4	after	after	ADP
american_scientific_journal-7486	28	5	its	its	PRON
american_scientific_journal-7486	28	6	discoverers	discoverer	NOUN
american_scientific_journal-7486	28	7	,	,	PUNCT
american_scientific_journal-7486	28	8	leonard	leonard	PROPN
american_scientific_journal-7486	28	9	adleman	adleman	PROPN
american_scientific_journal-7486	28	10	,	,	PUNCT
american_scientific_journal-7486	28	11	carl	carl	PROPN
american_scientific_journal-7486	28	12	pomerance	pomerance	NOUN
american_scientific_journal-7486	28	13	,	,	PUNCT
american_scientific_journal-7486	28	14	and	and	CCONJ
american_scientific_journal-7486	28	15	robert	robert	PROPN
american_scientific_journal-7486	28	16	rumely	rumely	ADV
american_scientific_journal-7486	28	17	and	and	CCONJ
american_scientific_journal-7486	28	18	later	later	ADV
american_scientific_journal-7486	28	19	improved	improve	VERB
american_scientific_journal-7486	28	20	by	by	ADP
american_scientific_journal-7486	28	21	henri	henri	PROPN
american_scientific_journal-7486	28	22	cohen	cohen	PROPN
american_scientific_journal-7486	28	23	and	and	CCONJ
american_scientific_journal-7486	28	24	hendrik	hendrik	PROPN
american_scientific_journal-7486	28	25	willem	willem	PROPN
american_scientific_journal-7486	28	26	lenstra	lenstra	PROPN
american_scientific_journal-7486	28	27	,	,	PUNCT
american_scientific_journal-7486	28	28	commonly	commonly	ADV
american_scientific_journal-7486	28	29	referred	refer	VERB
american_scientific_journal-7486	28	30	to	to	ADP
american_scientific_journal-7486	28	31	as	as	ADP
american_scientific_journal-7486	28	32	apr	apr	NOUN
american_scientific_journal-7486	28	33	-	-	PUNCT
american_scientific_journal-7486	28	34	cl	cl	NOUN
american_scientific_journal-7486	28	35	,	,	PUNCT
american_scientific_journal-7486	28	36	(	(	PUNCT
american_scientific_journal-7486	28	37	see	see	VERB
american_scientific_journal-7486	28	38	[	[	X
american_scientific_journal-7486	28	39	5	5	NUM
american_scientific_journal-7486	28	40	]	]	NUM
american_scientific_journal-7486	28	41	)	)	PUNCT
american_scientific_journal-7486	28	42	.	.	PUNCT
american_scientific_journal-7486	29	1	this	this	DET
american_scientific_journal-7486	29	2	article	article	NOUN
american_scientific_journal-7486	29	3	is	be	AUX
american_scientific_journal-7486	29	4	specifically	specifically	ADV
american_scientific_journal-7486	29	5	based	base	VERB
american_scientific_journal-7486	29	6	on	on	ADP
american_scientific_journal-7486	29	7	a	a	DET
american_scientific_journal-7486	29	8	novel	novel	NOUN
american_scientific_journal-7486	29	9	theorem	theorem	VERB
american_scientific_journal-7486	29	10	.	.	PUNCT
american_scientific_journal-7486	30	1	a	a	DET
american_scientific_journal-7486	30	2	new	new	ADJ
american_scientific_journal-7486	30	3	method	method	NOUN
american_scientific_journal-7486	30	4	is	be	AUX
american_scientific_journal-7486	30	5	devised	devise	VERB
american_scientific_journal-7486	30	6	,	,	PUNCT
american_scientific_journal-7486	30	7	adding	add	VERB
american_scientific_journal-7486	30	8	one	one	NUM
american_scientific_journal-7486	30	9	more	more	ADJ
american_scientific_journal-7486	30	10	probability	probability	NOUN
american_scientific_journal-7486	30	11	primality	primality	NOUN
american_scientific_journal-7486	30	12	test	test	NOUN
american_scientific_journal-7486	30	13	,	,	PUNCT
american_scientific_journal-7486	30	14	to	to	PART
american_scientific_journal-7486	30	15	check	check	VERB
american_scientific_journal-7486	30	16	whether	whether	SCONJ
american_scientific_journal-7486	30	17	a	a	DET
american_scientific_journal-7486	30	18	given	give	VERB
american_scientific_journal-7486	30	19	number	number	NOUN
american_scientific_journal-7486	30	20	is	be	AUX
american_scientific_journal-7486	30	21	a	a	DET
american_scientific_journal-7486	30	22	prime	prime	ADJ
american_scientific_journal-7486	30	23	number	number	NOUN
american_scientific_journal-7486	30	24	or	or	CCONJ
american_scientific_journal-7486	30	25	not	not	PART
american_scientific_journal-7486	30	26	.	.	PUNCT
american_scientific_journal-7486	31	1	in	in	ADP
american_scientific_journal-7486	31	2	the	the	DET
american_scientific_journal-7486	31	3	proof	proof	NOUN
american_scientific_journal-7486	31	4	,	,	PUNCT
american_scientific_journal-7486	31	5	the	the	DET
american_scientific_journal-7486	31	6	main	main	ADJ
american_scientific_journal-7486	31	7	notions	notion	NOUN
american_scientific_journal-7486	31	8	which	which	PRON
american_scientific_journal-7486	31	9	we	we	PRON
american_scientific_journal-7486	31	10	are	be	AUX
american_scientific_journal-7486	31	11	using	use	VERB
american_scientific_journal-7486	31	12	are	be	AUX
american_scientific_journal-7486	31	13	defined	define	VERB
american_scientific_journal-7486	31	14	as	as	SCONJ
american_scientific_journal-7486	31	15	follows	follow	VERB
american_scientific_journal-7486	31	16	:	:	PUNCT
american_scientific_journal-7486	31	17	1.1	1.1	NUM
american_scientific_journal-7486	31	18	definition	definition	NOUN
american_scientific_journal-7486	31	19	let	let	VERB
american_scientific_journal-7486	31	20	m	m	PRON
american_scientific_journal-7486	31	21	be	be	AUX
american_scientific_journal-7486	31	22	a	a	DET
american_scientific_journal-7486	31	23	fixed	fix	VERB
american_scientific_journal-7486	31	24	positive	positive	ADJ
american_scientific_journal-7486	31	25	integer	integer	NOUN
american_scientific_journal-7486	31	26	and	and	CCONJ
american_scientific_journal-7486	31	27	,	,	PUNCT
american_scientific_journal-7486	31	28	a	a	PRON
american_scientific_journal-7486	31	29	and	and	CCONJ
american_scientific_journal-7486	31	30	b	b	NOUN
american_scientific_journal-7486	31	31	be	be	AUX
american_scientific_journal-7486	31	32	any	any	DET
american_scientific_journal-7486	31	33	two	two	NUM
american_scientific_journal-7486	31	34	integers	integer	NOUN
american_scientific_journal-7486	31	35	.	.	PUNCT
american_scientific_journal-7486	32	1	if	if	SCONJ
american_scientific_journal-7486	32	2	m	m	VERB
american_scientific_journal-7486	32	3	|	|	ADV
american_scientific_journal-7486	32	4	(	(	PUNCT
american_scientific_journal-7486	32	5	b	b	X
american_scientific_journal-7486	32	6	−	−	NOUN
american_scientific_journal-7486	32	7	a	a	NOUN
american_scientific_journal-7486	32	8	)	)	PUNCT
american_scientific_journal-7486	32	9	,	,	PUNCT
american_scientific_journal-7486	32	10	we	we	PRON
american_scientific_journal-7486	32	11	say	say	VERB
american_scientific_journal-7486	32	12	that	that	SCONJ
american_scientific_journal-7486	32	13	a	a	PRON
american_scientific_journal-7486	32	14	is	be	AUX
american_scientific_journal-7486	32	15	congruent	congruent	ADJ
american_scientific_journal-7486	32	16	to	to	ADP
american_scientific_journal-7486	32	17	b	b	PROPN
american_scientific_journal-7486	32	18	modulo	modulo	NOUN
american_scientific_journal-7486	32	19	m	m	VERB
american_scientific_journal-7486	32	20	and	and	CCONJ
american_scientific_journal-7486	32	21	we	we	PRON
american_scientific_journal-7486	32	22	write	write	VERB
american_scientific_journal-7486	32	23	it	it	PRON
american_scientific_journal-7486	32	24	as	as	ADP
american_scientific_journal-7486	32	25	:	:	PUNCT
american_scientific_journal-7486	32	26	(	(	PUNCT
american_scientific_journal-7486	32	27	for	for	ADP
american_scientific_journal-7486	32	28	more	more	ADJ
american_scientific_journal-7486	32	29	see	see	NOUN
american_scientific_journal-7486	32	30	[	[	X
american_scientific_journal-7486	32	31	6	6	NUM
american_scientific_journal-7486	32	32	]	]	SYM
american_scientific_journal-7486	32	33	)	)	PUNCT
american_scientific_journal-7486	32	34	a	a	DET
american_scientific_journal-7486	32	35	≡	≡	PROPN
american_scientific_journal-7486	32	36	b(mod	b(mod	PROPN
american_scientific_journal-7486	32	37	m	m	PROPN
american_scientific_journal-7486	32	38	)	)	PUNCT
american_scientific_journal-7486	32	39	.	.	PUNCT
american_scientific_journal-7486	33	1	1.2	1.2	NUM
american_scientific_journal-7486	33	2	definition	definition	NOUN
american_scientific_journal-7486	33	3	let	let	VERB
american_scientific_journal-7486	33	4	s	s	PRON
american_scientific_journal-7486	33	5	=	=	PUNCT
american_scientific_journal-7486	33	6	{	{	PUNCT
american_scientific_journal-7486	33	7	a	a	PRON
american_scientific_journal-7486	33	8	,	,	PUNCT
american_scientific_journal-7486	33	9	b	b	NOUN
american_scientific_journal-7486	33	10	,	,	PUNCT
american_scientific_journal-7486	33	11	c	c	AUX
american_scientific_journal-7486	33	12	}	}	PUNCT
american_scientific_journal-7486	33	13	be	be	AUX
american_scientific_journal-7486	33	14	a	a	DET
american_scientific_journal-7486	33	15	set	set	NOUN
american_scientific_journal-7486	33	16	of	of	ADP
american_scientific_journal-7486	33	17	integers	integer	NOUN
american_scientific_journal-7486	33	18	(	(	PUNCT
american_scientific_journal-7486	33	19	z	z	NOUN
american_scientific_journal-7486	33	20	)	)	PUNCT
american_scientific_journal-7486	33	21	.	.	PUNCT
american_scientific_journal-7486	34	1	we	we	PRON
american_scientific_journal-7486	34	2	say	say	VERB
american_scientific_journal-7486	34	3	that	that	SCONJ
american_scientific_journal-7486	34	4	z	z	NOUN
american_scientific_journal-7486	34	5	is	be	AUX
american_scientific_journal-7486	34	6	equal	equal	ADJ
american_scientific_journal-7486	34	7	to	to	ADP
american_scientific_journal-7486	34	8	the	the	DET
american_scientific_journal-7486	34	9	union	union	NOUN
american_scientific_journal-7486	34	10	of	of	ADP
american_scientific_journal-7486	34	11	equivalence	equivalence	NOUN
american_scientific_journal-7486	34	12	of	of	ADP
american_scientific_journal-7486	34	13	the	the	DET
american_scientific_journal-7486	34	14	elements	element	NOUN
american_scientific_journal-7486	34	15	of	of	ADP
american_scientific_journal-7486	34	16	s	s	PRON
american_scientific_journal-7486	34	17	if	if	SCONJ
american_scientific_journal-7486	34	18	z	z	NOUN
american_scientific_journal-7486	34	19	=	=	PUNCT
american_scientific_journal-7486	35	1	[	[	X
american_scientific_journal-7486	35	2	a	a	X
american_scientific_journal-7486	35	3	]	]	X
american_scientific_journal-7486	35	4	∪	∪	ADP
american_scientific_journal-7486	35	5	[	[	X
american_scientific_journal-7486	35	6	b	b	X
american_scientific_journal-7486	35	7	]	]	X
american_scientific_journal-7486	35	8	∪	∪	ADP
american_scientific_journal-7486	35	9	[	[	X
american_scientific_journal-7486	35	10	c	c	X
american_scientific_journal-7486	35	11	]	]	X
american_scientific_journal-7486	35	12	,	,	PUNCT
american_scientific_journal-7486	35	13	where	where	SCONJ
american_scientific_journal-7486	35	14	[	[	X
american_scientific_journal-7486	35	15	.	.	X
american_scientific_journal-7486	35	16	]	]	PUNCT
american_scientific_journal-7486	35	17	denotes	denote	VERB
american_scientific_journal-7486	35	18	the	the	DET
american_scientific_journal-7486	35	19	equivalence	equivalence	NOUN
american_scientific_journal-7486	35	20	class	class	NOUN
american_scientific_journal-7486	35	21	(	(	PUNCT
american_scientific_journal-7486	35	22	see	see	VERB
american_scientific_journal-7486	35	23	[	[	X
american_scientific_journal-7486	35	24	7	7	NUM
american_scientific_journal-7486	35	25	]	]	NUM
american_scientific_journal-7486	35	26	)	)	PUNCT
american_scientific_journal-7486	35	27	.	.	PUNCT
american_scientific_journal-7486	36	1	2	2	X
american_scientific_journal-7486	36	2	.	.	X
american_scientific_journal-7486	36	3	methods	method	NOUN
american_scientific_journal-7486	36	4	and	and	CCONJ
american_scientific_journal-7486	36	5	main	main	ADJ
american_scientific_journal-7486	36	6	result	result	NOUN
american_scientific_journal-7486	36	7	in	in	ADP
american_scientific_journal-7486	36	8	this	this	DET
american_scientific_journal-7486	36	9	section	section	NOUN
american_scientific_journal-7486	36	10	,	,	PUNCT
american_scientific_journal-7486	36	11	we	we	PRON
american_scientific_journal-7486	36	12	prove	prove	VERB
american_scientific_journal-7486	36	13	our	our	PRON
american_scientific_journal-7486	36	14	main	main	ADJ
american_scientific_journal-7486	36	15	result	result	NOUN
american_scientific_journal-7486	36	16	.	.	PUNCT
american_scientific_journal-7486	37	1	2.1	2.1	NUM
american_scientific_journal-7486	37	2	:	:	PUNCT
american_scientific_journal-7486	37	3	theorem	theorem	VERB
american_scientific_journal-7486	37	4	.	.	PUNCT
american_scientific_journal-7486	38	1	every	every	DET
american_scientific_journal-7486	38	2	prime	prime	ADJ
american_scientific_journal-7486	38	3	number	number	NOUN
american_scientific_journal-7486	38	4	other	other	ADJ
american_scientific_journal-7486	38	5	than	than	ADP
american_scientific_journal-7486	38	6	2	2	NUM
american_scientific_journal-7486	38	7	and	and	CCONJ
american_scientific_journal-7486	38	8	3	3	NUM
american_scientific_journal-7486	38	9	satisfies	satisfie	NOUN
american_scientific_journal-7486	38	10	one	one	NUM
american_scientific_journal-7486	38	11	of	of	ADP
american_scientific_journal-7486	38	12	the	the	DET
american_scientific_journal-7486	38	13	following	follow	VERB
american_scientific_journal-7486	38	14	two	two	NUM
american_scientific_journal-7486	38	15	algebraic	algebraic	ADJ
american_scientific_journal-7486	38	16	expressions	expression	NOUN
american_scientific_journal-7486	38	17	:	:	PUNCT
american_scientific_journal-7486	38	18	x	x	SYM
american_scientific_journal-7486	38	19	−	−	PROPN
american_scientific_journal-7486	38	20	n90	n90	NOUN
american_scientific_journal-7486	38	21	−	−	PROPN
american_scientific_journal-7486	38	22	5	5	NUM
american_scientific_journal-7486	38	23	=	=	SYM
american_scientific_journal-7486	38	24	6	6	NUM
american_scientific_journal-7486	38	25	m	m	NOUN
american_scientific_journal-7486	38	26	or	or	CCONJ
american_scientific_journal-7486	38	27	x	x	SYM
american_scientific_journal-7486	38	28	−	−	PROPN
american_scientific_journal-7486	38	29	n90	n90	PROPN
american_scientific_journal-7486	38	30	−	−	PROPN
american_scientific_journal-7486	38	31	7	7	NUM
american_scientific_journal-7486	38	32	=	=	SYM
american_scientific_journal-7486	38	33	6	6	NUM
american_scientific_journal-7486	38	34	m	m	NOUN
american_scientific_journal-7486	38	35	https://en.wikipedia.org/wiki/deterministic_algorithm	https://en.wikipedia.org/wiki/deterministic_algorithm	NOUN
american_scientific_journal-7486	38	36	https://en.wikipedia.org/wiki/primality_test	https://en.wikipedia.org/wiki/primality_t	ADJ
american_scientific_journal-7486	38	37	https://en.wikipedia.org/wiki/algorithm	https://en.wikipedia.org/wiki/algorithm	PROPN
american_scientific_journal-7486	38	38	https://en.wikipedia.org/wiki/manindra_agrawal	https://en.wikipedia.org/wiki/manindra_agrawal	VERB
american_scientific_journal-7486	38	39	https://en.wikipedia.org/wiki/neeraj_kayal	https://en.wikipedia.org/wiki/neeraj_kayal	NOUN
american_scientific_journal-7486	38	40	https://en.wikipedia.org/wiki/nitin_saxena	https://en.wikipedia.org/wiki/nitin_saxena	PROPN
american_scientific_journal-7486	38	41	https://en.wikipedia.org/wiki/computational_number_theory	https://en.wikipedia.org/wiki/computational_number_theory	X
american_scientific_journal-7486	38	42	https://en.wikipedia.org/wiki/algorithm	https://en.wikipedia.org/wiki/algorithm	PROPN
american_scientific_journal-7486	38	43	https://en.wikipedia.org/wiki/prime_number	https://en.wikipedia.org/wiki/prime_number	PROPN
american_scientific_journal-7486	38	44	https://en.wikipedia.org/wiki/leonard_adleman	https://en.wikipedia.org/wiki/leonard_adleman	NOUN
american_scientific_journal-7486	38	45	https://en.wikipedia.org/wiki/carl_pomerance	https://en.wikipedia.org/wiki/carl_pomerance	PROPN
american_scientific_journal-7486	38	46	https://en.wikipedia.org/wiki/robert_rumely	https://en.wikipedia.org/wiki/robert_rumely	ADV
american_scientific_journal-7486	38	47	https://en.wikipedia.org/wiki/henri_cohen_(number_theorist	https://en.wikipedia.org/wiki/henri_cohen_(number_theorist	NUM
american_scientific_journal-7486	38	48	)	)	PUNCT
american_scientific_journal-7486	38	49	https://en.wikipedia.org/wiki/hendrik_willem_lenstra	https://en.wikipedia.org/wiki/hendrik_willem_lenstra	PROPN
american_scientific_journal-7486	38	50	american	american	ADJ
american_scientific_journal-7486	38	51	academic	academic	ADJ
american_scientific_journal-7486	38	52	scientific	scientific	ADJ
american_scientific_journal-7486	38	53	research	research	NOUN
american_scientific_journal-7486	38	54	journal	journal	NOUN
american_scientific_journal-7486	38	55	for	for	ADP
american_scientific_journal-7486	38	56	engineering	engineering	NOUN
american_scientific_journal-7486	38	57	,	,	PUNCT
american_scientific_journal-7486	38	58	technology	technology	NOUN
american_scientific_journal-7486	38	59	,	,	PUNCT
american_scientific_journal-7486	38	60	and	and	CCONJ
american_scientific_journal-7486	38	61	sciences	science	NOUN
american_scientific_journal-7486	38	62	(	(	PUNCT
american_scientific_journal-7486	38	63	asrjets	asrjet	NOUN
american_scientific_journal-7486	38	64	)	)	PUNCT
american_scientific_journal-7486	38	65	(	(	PUNCT
american_scientific_journal-7486	38	66	2022	2022	NUM
american_scientific_journal-7486	38	67	)	)	PUNCT
american_scientific_journal-7486	38	68	volume	volume	NOUN
american_scientific_journal-7486	38	69	88	88	NUM
american_scientific_journal-7486	38	70	,	,	PUNCT
american_scientific_journal-7486	38	71	no	no	DET
american_scientific_journal-7486	38	72	1	1	NUM
american_scientific_journal-7486	38	73	,	,	PUNCT
american_scientific_journal-7486	38	74	pp	pp	ADV
american_scientific_journal-7486	38	75	77	77	NUM
american_scientific_journal-7486	38	76	-	-	SYM
american_scientific_journal-7486	38	77	90	90	NUM
american_scientific_journal-7486	38	78	79	79	NUM
american_scientific_journal-7486	38	79	where	where	SCONJ
american_scientific_journal-7486	38	80	n90	n90	PROPN
american_scientific_journal-7486	38	81	is	be	AUX
american_scientific_journal-7486	38	82	the	the	DET
american_scientific_journal-7486	38	83	nearest	near	ADJ
american_scientific_journal-7486	38	84	multiple	multiple	NOUN
american_scientific_journal-7486	38	85	of	of	ADP
american_scientific_journal-7486	38	86	90	90	NUM
american_scientific_journal-7486	38	87	and	and	CCONJ
american_scientific_journal-7486	38	88	m	m	PROPN
american_scientific_journal-7486	38	89	is	be	AUX
american_scientific_journal-7486	38	90	a	a	DET
american_scientific_journal-7486	38	91	whole	whole	ADJ
american_scientific_journal-7486	38	92	number	number	NOUN
american_scientific_journal-7486	38	93	.	.	PUNCT
american_scientific_journal-7486	39	1	2.2	2.2	NUM
american_scientific_journal-7486	39	2	:	:	PUNCT
american_scientific_journal-7486	39	3	proof	proof	NOUN
american_scientific_journal-7486	39	4	let	let	VERB
american_scientific_journal-7486	39	5	x	x	PRON
american_scientific_journal-7486	39	6	>	>	X
american_scientific_journal-7486	39	7	1	1	NUM
american_scientific_journal-7486	39	8	be	be	AUX
american_scientific_journal-7486	39	9	a	a	DET
american_scientific_journal-7486	39	10	positive	positive	ADJ
american_scientific_journal-7486	39	11	integer	integer	NOUN
american_scientific_journal-7486	39	12	,	,	PUNCT
american_scientific_journal-7486	39	13	then	then	ADV
american_scientific_journal-7486	39	14	we	we	PRON
american_scientific_journal-7486	39	15	have	have	VERB
american_scientific_journal-7486	39	16	to	to	PART
american_scientific_journal-7486	39	17	show	show	VERB
american_scientific_journal-7486	39	18	that	that	SCONJ
american_scientific_journal-7486	39	19	,	,	PUNCT
american_scientific_journal-7486	39	20	if	if	SCONJ
american_scientific_journal-7486	39	21	x	x	PRON
american_scientific_journal-7486	39	22	is	be	AUX
american_scientific_journal-7486	39	23	a	a	DET
american_scientific_journal-7486	39	24	prime	prime	ADJ
american_scientific_journal-7486	39	25	number	number	NOUN
american_scientific_journal-7486	39	26	,	,	PUNCT
american_scientific_journal-7486	39	27	then	then	ADV
american_scientific_journal-7486	39	28	it	it	PRON
american_scientific_journal-7486	39	29	satisfies	satisfy	VERB
american_scientific_journal-7486	39	30	x	x	PUNCT
american_scientific_journal-7486	39	31	−	−	PROPN
american_scientific_journal-7486	39	32	n90	n90	PROPN
american_scientific_journal-7486	39	33	−	−	PROPN
american_scientific_journal-7486	39	34	5	5	NUM
american_scientific_journal-7486	39	35	=	=	SYM
american_scientific_journal-7486	39	36	6	6	NUM
american_scientific_journal-7486	39	37	m	m	NOUN
american_scientific_journal-7486	39	38	or	or	CCONJ
american_scientific_journal-7486	39	39	x	x	SYM
american_scientific_journal-7486	39	40	−	−	PROPN
american_scientific_journal-7486	39	41	n90	n90	PROPN
american_scientific_journal-7486	39	42	−	−	PROPN
american_scientific_journal-7486	39	43	7	7	NUM
american_scientific_journal-7486	39	44	=	=	SYM
american_scientific_journal-7486	39	45	6	6	NUM
american_scientific_journal-7486	39	46	m	m	NOUN
american_scientific_journal-7486	39	47	case	case	NOUN
american_scientific_journal-7486	39	48	studies	study	NOUN
american_scientific_journal-7486	39	49	we	we	PRON
american_scientific_journal-7486	39	50	will	will	AUX
american_scientific_journal-7486	39	51	consider	consider	VERB
american_scientific_journal-7486	39	52	both	both	CCONJ
american_scientific_journal-7486	39	53	the	the	DET
american_scientific_journal-7486	39	54	expressions	expression	NOUN
american_scientific_journal-7486	39	55	one	one	NUM
american_scientific_journal-7486	39	56	by	by	ADP
american_scientific_journal-7486	39	57	one	one	NUM
american_scientific_journal-7486	39	58	.	.	PUNCT
american_scientific_journal-7486	40	1	case	case	NOUN
american_scientific_journal-7486	40	2	1	1	NUM
american_scientific_journal-7486	40	3	consider	consider	VERB
american_scientific_journal-7486	40	4	x	x	X
american_scientific_journal-7486	40	5	−	−	PROPN
american_scientific_journal-7486	40	6	n90	n90	PROPN
american_scientific_journal-7486	40	7	−	−	PROPN
american_scientific_journal-7486	40	8	5	5	NUM
american_scientific_journal-7486	40	9	=	=	SYM
american_scientific_journal-7486	40	10	6	6	NUM
american_scientific_journal-7486	40	11	m	m	NOUN
american_scientific_journal-7486	40	12	,	,	PUNCT
american_scientific_journal-7486	40	13	where	where	SCONJ
american_scientific_journal-7486	40	14	m	m	NOUN
american_scientific_journal-7486	40	15	is	be	AUX
american_scientific_journal-7486	40	16	a	a	DET
american_scientific_journal-7486	40	17	whole	whole	ADJ
american_scientific_journal-7486	40	18	number	number	NOUN
american_scientific_journal-7486	40	19	.	.	PUNCT
american_scientific_journal-7486	41	1	from	from	ADP
american_scientific_journal-7486	41	2	the	the	DET
american_scientific_journal-7486	41	3	above	above	ADJ
american_scientific_journal-7486	41	4	statement	statement	NOUN
american_scientific_journal-7486	41	5	,	,	PUNCT
american_scientific_journal-7486	41	6	we	we	PRON
american_scientific_journal-7486	41	7	can	can	AUX
american_scientific_journal-7486	41	8	say	say	VERB
american_scientific_journal-7486	41	9	that	that	SCONJ
american_scientific_journal-7486	41	10	6	6	NUM
american_scientific_journal-7486	41	11	is	be	AUX
american_scientific_journal-7486	41	12	dividing	divide	VERB
american_scientific_journal-7486	41	13	x	x	PUNCT
american_scientific_journal-7486	41	14	−	−	PROPN
american_scientific_journal-7486	41	15	n90	n90	PROPN
american_scientific_journal-7486	41	16	−	−	PROPN
american_scientific_journal-7486	41	17	5	5	NUM
american_scientific_journal-7486	41	18	perfectly	perfectly	ADV
american_scientific_journal-7486	41	19	.	.	PUNCT
american_scientific_journal-7486	42	1	in	in	ADP
american_scientific_journal-7486	42	2	other	other	ADJ
american_scientific_journal-7486	42	3	words	word	NOUN
american_scientific_journal-7486	42	4	,	,	PUNCT
american_scientific_journal-7486	42	5	using	use	VERB
american_scientific_journal-7486	42	6	the	the	DET
american_scientific_journal-7486	42	7	notion	notion	NOUN
american_scientific_journal-7486	42	8	of	of	ADP
american_scientific_journal-7486	42	9	congruence	congruence	NOUN
american_scientific_journal-7486	42	10	modulo	modulo	NOUN
american_scientific_journal-7486	42	11	,	,	PUNCT
american_scientific_journal-7486	42	12	we	we	PRON
american_scientific_journal-7486	42	13	can	can	AUX
american_scientific_journal-7486	42	14	write	write	VERB
american_scientific_journal-7486	42	15	:	:	PUNCT
american_scientific_journal-7486	42	16	x	x	PUNCT
american_scientific_journal-7486	42	17	−	−	PROPN
american_scientific_journal-7486	42	18	n90	n90	PROPN
american_scientific_journal-7486	42	19	−	−	PROPN
american_scientific_journal-7486	42	20	5	5	NUM
american_scientific_journal-7486	42	21	≡	≡	PROPN
american_scientific_journal-7486	42	22	0(mod	0(mod	NOUN
american_scientific_journal-7486	42	23	6	6	NUM
american_scientific_journal-7486	42	24	)	)	PUNCT
american_scientific_journal-7486	42	25	.	.	PUNCT
american_scientific_journal-7486	43	1	from	from	ADP
american_scientific_journal-7486	43	2	above	above	ADP
american_scientific_journal-7486	43	3	congruence	congruence	NOUN
american_scientific_journal-7486	43	4	,	,	PUNCT
american_scientific_journal-7486	43	5	we	we	PRON
american_scientific_journal-7486	43	6	get	get	VERB
american_scientific_journal-7486	43	7	:	:	PUNCT
american_scientific_journal-7486	43	8	x	x	SYM
american_scientific_journal-7486	43	9	−	−	PROPN
american_scientific_journal-7486	43	10	5	5	NUM
american_scientific_journal-7486	43	11	≡	≡	PROPN
american_scientific_journal-7486	43	12	0(mod	0(mod	NOUN
american_scientific_journal-7486	43	13	6	6	NUM
american_scientific_journal-7486	43	14	)	)	PUNCT
american_scientific_journal-7486	43	15	,	,	PUNCT
american_scientific_journal-7486	43	16	or	or	CCONJ
american_scientific_journal-7486	43	17	x	x	ADP
american_scientific_journal-7486	43	18	≡	≡	ADJ
american_scientific_journal-7486	43	19	5(mod	5(mod	NOUN
american_scientific_journal-7486	43	20	6	6	NUM
american_scientific_journal-7486	43	21	)	)	PUNCT
american_scientific_journal-7486	43	22	.	.	PUNCT
american_scientific_journal-7486	44	1	(	(	PUNCT
american_scientific_journal-7486	44	2	2.2.1	2.2.1	NUM
american_scientific_journal-7486	44	3	)	)	PUNCT
american_scientific_journal-7486	44	4	case	case	NOUN
american_scientific_journal-7486	44	5	2	2	NUM
american_scientific_journal-7486	44	6	consider	consider	VERB
american_scientific_journal-7486	44	7	x	x	X
american_scientific_journal-7486	44	8	−	−	PROPN
american_scientific_journal-7486	44	9	n90	n90	PROPN
american_scientific_journal-7486	44	10	−	−	PROPN
american_scientific_journal-7486	44	11	7	7	NUM
american_scientific_journal-7486	44	12	=	=	SYM
american_scientific_journal-7486	44	13	6	6	NUM
american_scientific_journal-7486	44	14	m.	m.	NOUN
american_scientific_journal-7486	44	15	from	from	ADP
american_scientific_journal-7486	44	16	the	the	DET
american_scientific_journal-7486	44	17	above	above	ADJ
american_scientific_journal-7486	44	18	statement	statement	NOUN
american_scientific_journal-7486	44	19	,	,	PUNCT
american_scientific_journal-7486	44	20	we	we	PRON
american_scientific_journal-7486	44	21	can	can	AUX
american_scientific_journal-7486	44	22	say	say	VERB
american_scientific_journal-7486	44	23	that	that	SCONJ
american_scientific_journal-7486	44	24	6	6	NUM
american_scientific_journal-7486	44	25	is	be	AUX
american_scientific_journal-7486	44	26	dividing	divide	VERB
american_scientific_journal-7486	44	27	x	x	PUNCT
american_scientific_journal-7486	44	28	−	−	PROPN
american_scientific_journal-7486	44	29	n90	n90	PROPN
american_scientific_journal-7486	44	30	−	−	PROPN
american_scientific_journal-7486	44	31	7	7	NUM
american_scientific_journal-7486	44	32	perfectly	perfectly	ADV
american_scientific_journal-7486	44	33	.	.	PUNCT
american_scientific_journal-7486	45	1	using	use	VERB
american_scientific_journal-7486	45	2	the	the	DET
american_scientific_journal-7486	45	3	notion	notion	NOUN
american_scientific_journal-7486	45	4	of	of	ADP
american_scientific_journal-7486	45	5	congruence	congruence	NOUN
american_scientific_journal-7486	45	6	modulo	modulo	NOUN
american_scientific_journal-7486	45	7	,	,	PUNCT
american_scientific_journal-7486	45	8	we	we	PRON
american_scientific_journal-7486	45	9	can	can	AUX
american_scientific_journal-7486	45	10	write	write	VERB
american_scientific_journal-7486	45	11	:	:	PUNCT
american_scientific_journal-7486	45	12	x	x	PUNCT
american_scientific_journal-7486	45	13	−	−	PROPN
american_scientific_journal-7486	45	14	n90	n90	PROPN
american_scientific_journal-7486	45	15	−	−	PROPN
american_scientific_journal-7486	45	16	7	7	NUM
american_scientific_journal-7486	45	17	≡	≡	PROPN
american_scientific_journal-7486	45	18	0(mod	0(mod	NOUN
american_scientific_journal-7486	45	19	6	6	NUM
american_scientific_journal-7486	45	20	)	)	PUNCT
american_scientific_journal-7486	45	21	.	.	PUNCT
american_scientific_journal-7486	46	1	american	american	ADJ
american_scientific_journal-7486	46	2	academic	academic	ADJ
american_scientific_journal-7486	46	3	scientific	scientific	ADJ
american_scientific_journal-7486	46	4	research	research	NOUN
american_scientific_journal-7486	46	5	journal	journal	NOUN
american_scientific_journal-7486	46	6	for	for	ADP
american_scientific_journal-7486	46	7	engineering	engineering	NOUN
american_scientific_journal-7486	46	8	,	,	PUNCT
american_scientific_journal-7486	46	9	technology	technology	NOUN
american_scientific_journal-7486	46	10	,	,	PUNCT
american_scientific_journal-7486	46	11	and	and	CCONJ
american_scientific_journal-7486	46	12	sciences	science	NOUN
american_scientific_journal-7486	46	13	(	(	PUNCT
american_scientific_journal-7486	46	14	asrjets	asrjet	NOUN
american_scientific_journal-7486	46	15	)	)	PUNCT
american_scientific_journal-7486	46	16	(	(	PUNCT
american_scientific_journal-7486	46	17	2022	2022	NUM
american_scientific_journal-7486	46	18	)	)	PUNCT
american_scientific_journal-7486	46	19	volume	volume	NOUN
american_scientific_journal-7486	46	20	88	88	NUM
american_scientific_journal-7486	46	21	,	,	PUNCT
american_scientific_journal-7486	46	22	no	no	DET
american_scientific_journal-7486	46	23	1	1	NUM
american_scientific_journal-7486	46	24	,	,	PUNCT
american_scientific_journal-7486	46	25	pp	pp	ADV
american_scientific_journal-7486	46	26	77	77	NUM
american_scientific_journal-7486	46	27	-	-	SYM
american_scientific_journal-7486	46	28	90	90	NUM
american_scientific_journal-7486	46	29	80	80	NUM
american_scientific_journal-7486	46	30	this	this	PRON
american_scientific_journal-7486	46	31	implies	imply	VERB
american_scientific_journal-7486	46	32	that	that	SCONJ
american_scientific_journal-7486	46	33	:	:	PUNCT
american_scientific_journal-7486	46	34	x	x	X
american_scientific_journal-7486	47	1	−	−	PROPN
american_scientific_journal-7486	47	2	7	7	NUM
american_scientific_journal-7486	47	3	≡	≡	PROPN
american_scientific_journal-7486	47	4	0(mod	0(mod	NOUN
american_scientific_journal-7486	47	5	6	6	NUM
american_scientific_journal-7486	47	6	)	)	PUNCT
american_scientific_journal-7486	47	7	.	.	PUNCT
american_scientific_journal-7486	48	1	the	the	DET
american_scientific_journal-7486	48	2	above	above	ADJ
american_scientific_journal-7486	48	3	congruence	congruence	NOUN
american_scientific_journal-7486	48	4	can	can	AUX
american_scientific_journal-7486	48	5	be	be	AUX
american_scientific_journal-7486	48	6	written	write	VERB
american_scientific_journal-7486	48	7	as	as	ADP
american_scientific_journal-7486	48	8	:	:	PUNCT
american_scientific_journal-7486	48	9	x	x	NUM
american_scientific_journal-7486	48	10	≡	≡	PROPN
american_scientific_journal-7486	48	11	7(mod	7(mod	NUM
american_scientific_journal-7486	48	12	6	6	NUM
american_scientific_journal-7486	48	13	)	)	PUNCT
american_scientific_journal-7486	48	14	,	,	PUNCT
american_scientific_journal-7486	48	15	or	or	CCONJ
american_scientific_journal-7486	48	16	x	x	X
american_scientific_journal-7486	48	17	≡	≡	PROPN
american_scientific_journal-7486	48	18	1(mod	1(mod	NUM
american_scientific_journal-7486	48	19	6	6	NUM
american_scientific_journal-7486	48	20	)	)	PUNCT
american_scientific_journal-7486	48	21	.	.	PUNCT
american_scientific_journal-7486	49	1	(	(	PUNCT
american_scientific_journal-7486	49	2	2.2.2	2.2.2	X
american_scientific_journal-7486	49	3	)	)	PUNCT
american_scientific_journal-7486	49	4	now	now	ADV
american_scientific_journal-7486	49	5	,	,	PUNCT
american_scientific_journal-7486	49	6	we	we	PRON
american_scientific_journal-7486	49	7	form	form	VERB
american_scientific_journal-7486	49	8	equivalence	equivalence	NOUN
american_scientific_journal-7486	49	9	classes	class	NOUN
american_scientific_journal-7486	49	10	of	of	ADP
american_scientific_journal-7486	49	11	integers	integer	NOUN
american_scientific_journal-7486	49	12	with	with	ADP
american_scientific_journal-7486	49	13	the	the	DET
american_scientific_journal-7486	49	14	help	help	NOUN
american_scientific_journal-7486	49	15	of	of	ADP
american_scientific_journal-7486	49	16	elements	element	NOUN
american_scientific_journal-7486	49	17	of	of	ADP
american_scientific_journal-7486	49	18	the	the	DET
american_scientific_journal-7486	49	19	following	follow	VERB
american_scientific_journal-7486	49	20	set	set	NOUN
american_scientific_journal-7486	49	21	:	:	PUNCT
american_scientific_journal-7486	49	22	s	s	X
american_scientific_journal-7486	49	23	=	=	PUNCT
american_scientific_journal-7486	49	24	{	{	PUNCT
american_scientific_journal-7486	49	25	6n	6n	PROPN
american_scientific_journal-7486	49	26	,	,	PUNCT
american_scientific_journal-7486	49	27	6n	6n	NOUN
american_scientific_journal-7486	50	1	+	+	CCONJ
american_scientific_journal-7486	50	2	1	1	NUM
american_scientific_journal-7486	50	3	,	,	PUNCT
american_scientific_journal-7486	50	4	6n	6n	NOUN
american_scientific_journal-7486	50	5	+	+	CCONJ
american_scientific_journal-7486	50	6	2	2	NUM
american_scientific_journal-7486	50	7	,	,	PUNCT
american_scientific_journal-7486	50	8	6n	6n	NOUN
american_scientific_journal-7486	50	9	+	+	CCONJ
american_scientific_journal-7486	50	10	3	3	NUM
american_scientific_journal-7486	50	11	,	,	PUNCT
american_scientific_journal-7486	50	12	6n	6n	NOUN
american_scientific_journal-7486	50	13	+	+	CCONJ
american_scientific_journal-7486	50	14	4	4	NUM
american_scientific_journal-7486	50	15	,	,	PUNCT
american_scientific_journal-7486	50	16	6n	6n	NOUN
american_scientific_journal-7486	50	17	+	+	CCONJ
american_scientific_journal-7486	50	18	5	5	NUM
american_scientific_journal-7486	50	19	}	}	PUNCT
american_scientific_journal-7486	50	20	,	,	PUNCT
american_scientific_journal-7486	50	21	where	where	SCONJ
american_scientific_journal-7486	50	22	n	n	X
american_scientific_journal-7486	50	23	∈	∈	PROPN
american_scientific_journal-7486	50	24	z.	z.	PROPN
american_scientific_journal-7486	50	25	it	it	PRON
american_scientific_journal-7486	50	26	is	be	AUX
american_scientific_journal-7486	50	27	straightforward	straightforward	ADJ
american_scientific_journal-7486	50	28	to	to	PART
american_scientific_journal-7486	50	29	check	check	VERB
american_scientific_journal-7486	50	30	that	that	PRON
american_scientific_journal-7486	50	31	z	z	NOUN
american_scientific_journal-7486	51	1	=	=	PUNCT
american_scientific_journal-7486	52	1	[	[	X
american_scientific_journal-7486	52	2	6n	6n	X
american_scientific_journal-7486	52	3	]	]	PUNCT
american_scientific_journal-7486	52	4	∪	∪	ADP
american_scientific_journal-7486	52	5	[	[	PUNCT
american_scientific_journal-7486	52	6	6n+	6n+	NUM
american_scientific_journal-7486	52	7	1	1	NUM
american_scientific_journal-7486	52	8	]	]	PUNCT
american_scientific_journal-7486	52	9	∪	∪	ADP
american_scientific_journal-7486	52	10	[	[	PUNCT
american_scientific_journal-7486	52	11	6n+	6n+	NUM
american_scientific_journal-7486	52	12	2	2	NUM
american_scientific_journal-7486	52	13	]	]	PUNCT
american_scientific_journal-7486	52	14	∪	∪	ADP
american_scientific_journal-7486	52	15	[	[	X
american_scientific_journal-7486	52	16	6n	6n	NOUN
american_scientific_journal-7486	52	17	+	+	CCONJ
american_scientific_journal-7486	52	18	3	3	X
american_scientific_journal-7486	52	19	]	]	PUNCT
american_scientific_journal-7486	52	20	∪	∪	ADP
american_scientific_journal-7486	52	21	[	[	X
american_scientific_journal-7486	52	22	6n	6n	NOUN
american_scientific_journal-7486	52	23	+	+	CCONJ
american_scientific_journal-7486	52	24	4	4	NUM
american_scientific_journal-7486	52	25	]	]	PUNCT
american_scientific_journal-7486	52	26	∪	∪	ADP
american_scientific_journal-7486	52	27	[	[	X
american_scientific_journal-7486	52	28	6n	6n	NOUN
american_scientific_journal-7486	52	29	+	+	CCONJ
american_scientific_journal-7486	52	30	5	5	NUM
american_scientific_journal-7486	52	31	]	]	PUNCT
american_scientific_journal-7486	52	32	.	.	PUNCT
american_scientific_journal-7486	53	1	this	this	PRON
american_scientific_journal-7486	53	2	means	mean	VERB
american_scientific_journal-7486	53	3	that	that	SCONJ
american_scientific_journal-7486	53	4	z	z	NOUN
american_scientific_journal-7486	53	5	is	be	AUX
american_scientific_journal-7486	53	6	equal	equal	ADJ
american_scientific_journal-7486	53	7	to	to	ADP
american_scientific_journal-7486	53	8	the	the	DET
american_scientific_journal-7486	53	9	disjoint	disjoint	PROPN
american_scientific_journal-7486	53	10	union	union	NOUN
american_scientific_journal-7486	53	11	of	of	ADP
american_scientific_journal-7486	53	12	the	the	DET
american_scientific_journal-7486	53	13	equivalence	equivalence	NOUN
american_scientific_journal-7486	53	14	classes	class	NOUN
american_scientific_journal-7486	53	15	of	of	ADP
american_scientific_journal-7486	53	16	elements	element	NOUN
american_scientific_journal-7486	53	17	of	of	ADP
american_scientific_journal-7486	53	18	s.	s.	PROPN
american_scientific_journal-7486	53	19	therefore	therefore	ADV
american_scientific_journal-7486	53	20	,	,	PUNCT
american_scientific_journal-7486	53	21	s	s	PROPN
american_scientific_journal-7486	53	22	gives	give	VERB
american_scientific_journal-7486	53	23	us	we	PRON
american_scientific_journal-7486	53	24	the	the	DET
american_scientific_journal-7486	53	25	set	set	NOUN
american_scientific_journal-7486	53	26	of	of	ADP
american_scientific_journal-7486	53	27	all	all	DET
american_scientific_journal-7486	53	28	integers	integer	NOUN
american_scientific_journal-7486	53	29	.	.	PUNCT
american_scientific_journal-7486	54	1	out	out	ADP
american_scientific_journal-7486	54	2	of	of	ADP
american_scientific_journal-7486	54	3	the	the	DET
american_scientific_journal-7486	54	4	s	s	PROPN
american_scientific_journal-7486	54	5	,	,	PUNCT
american_scientific_journal-7486	54	6	the	the	DET
american_scientific_journal-7486	54	7	elements	element	NOUN
american_scientific_journal-7486	54	8	given	give	VERB
american_scientific_journal-7486	54	9	by	by	ADP
american_scientific_journal-7486	54	10	the	the	DET
american_scientific_journal-7486	54	11	equivalence	equivalence	NOUN
american_scientific_journal-7486	54	12	classes	class	NOUN
american_scientific_journal-7486	55	1	[	[	X
american_scientific_journal-7486	55	2	6n	6n	NOUN
american_scientific_journal-7486	55	3	]	]	PUNCT
american_scientific_journal-7486	55	4	,	,	PUNCT
american_scientific_journal-7486	56	1	[	[	X
american_scientific_journal-7486	56	2	6n+2	6n+2	NUM
american_scientific_journal-7486	56	3	]	]	PUNCT
american_scientific_journal-7486	56	4	,	,	PUNCT
american_scientific_journal-7486	56	5	[	[	X
american_scientific_journal-7486	56	6	6n+3	6n+3	NOUN
american_scientific_journal-7486	56	7	]	]	PUNCT
american_scientific_journal-7486	56	8	and	and	CCONJ
american_scientific_journal-7486	56	9	[	[	X
american_scientific_journal-7486	56	10	6n+4	6n+4	NOUN
american_scientific_journal-7486	56	11	]	]	PUNCT
american_scientific_journal-7486	56	12	are	be	AUX
american_scientific_journal-7486	56	13	composite	composite	ADJ
american_scientific_journal-7486	56	14	numbers	number	NOUN
american_scientific_journal-7486	56	15	.	.	PUNCT
american_scientific_journal-7486	57	1	then	then	ADV
american_scientific_journal-7486	57	2	the	the	DET
american_scientific_journal-7486	57	3	possible	possible	ADJ
american_scientific_journal-7486	57	4	choice	choice	NOUN
american_scientific_journal-7486	57	5	for	for	ADP
american_scientific_journal-7486	57	6	a	a	DET
american_scientific_journal-7486	57	7	number	number	NOUN
american_scientific_journal-7486	57	8	(	(	PUNCT
american_scientific_journal-7486	57	9	except	except	SCONJ
american_scientific_journal-7486	57	10	2	2	NUM
american_scientific_journal-7486	57	11	and	and	CCONJ
american_scientific_journal-7486	57	12	3	3	NUM
american_scientific_journal-7486	57	13	)	)	PUNCT
american_scientific_journal-7486	57	14	to	to	PART
american_scientific_journal-7486	57	15	be	be	AUX
american_scientific_journal-7486	57	16	a	a	DET
american_scientific_journal-7486	57	17	prime	prime	ADJ
american_scientific_journal-7486	57	18	number	number	NOUN
american_scientific_journal-7486	57	19	is	be	AUX
american_scientific_journal-7486	57	20	that	that	SCONJ
american_scientific_journal-7486	57	21	the	the	DET
american_scientific_journal-7486	57	22	number	number	NOUN
american_scientific_journal-7486	57	23	is	be	AUX
american_scientific_journal-7486	57	24	in	in	ADP
american_scientific_journal-7486	57	25	[	[	X
american_scientific_journal-7486	57	26	6n	6n	NOUN
american_scientific_journal-7486	57	27	+	+	CCONJ
american_scientific_journal-7486	57	28	1	1	NUM
american_scientific_journal-7486	57	29	]	]	PUNCT
american_scientific_journal-7486	57	30	or	or	CCONJ
american_scientific_journal-7486	57	31	[	[	X
american_scientific_journal-7486	57	32	6n	6n	NOUN
american_scientific_journal-7486	57	33	+	+	CCONJ
american_scientific_journal-7486	57	34	5	5	NUM
american_scientific_journal-7486	57	35	]	]	PUNCT
american_scientific_journal-7486	57	36	.	.	PUNCT
american_scientific_journal-7486	58	1	it	it	PRON
american_scientific_journal-7486	58	2	is	be	AUX
american_scientific_journal-7486	58	3	then	then	ADV
american_scientific_journal-7486	58	4	easy	easy	ADJ
american_scientific_journal-7486	58	5	to	to	PART
american_scientific_journal-7486	58	6	check	check	VERB
american_scientific_journal-7486	58	7	that	that	SCONJ
american_scientific_journal-7486	58	8	an	an	DET
american_scientific_journal-7486	58	9	element	element	NOUN
american_scientific_journal-7486	58	10	x	x	X
american_scientific_journal-7486	58	11	∈	∈	PROPN
american_scientific_journal-7486	59	1	[	[	X
american_scientific_journal-7486	59	2	6n	6n	NOUN
american_scientific_journal-7486	59	3	+	+	CCONJ
american_scientific_journal-7486	59	4	1	1	NUM
american_scientific_journal-7486	59	5	]	]	X
american_scientific_journal-7486	59	6	if	if	SCONJ
american_scientific_journal-7486	59	7	and	and	CCONJ
american_scientific_journal-7486	59	8	only	only	ADV
american_scientific_journal-7486	59	9	if	if	SCONJ
american_scientific_journal-7486	59	10	x	x	SYM
american_scientific_journal-7486	59	11	≡	≡	PROPN
american_scientific_journal-7486	59	12	1(mod	1(mod	NUM
american_scientific_journal-7486	59	13	6	6	NUM
american_scientific_journal-7486	59	14	)	)	PUNCT
american_scientific_journal-7486	59	15	.	.	PUNCT
american_scientific_journal-7486	60	1	similarly	similarly	ADV
american_scientific_journal-7486	60	2	,	,	PUNCT
american_scientific_journal-7486	60	3	x	x	PUNCT
american_scientific_journal-7486	60	4	∈	∈	PROPN
american_scientific_journal-7486	61	1	[	[	X
american_scientific_journal-7486	61	2	6n	6n	NOUN
american_scientific_journal-7486	61	3	+	+	CCONJ
american_scientific_journal-7486	61	4	5	5	NUM
american_scientific_journal-7486	61	5	]	]	X
american_scientific_journal-7486	61	6	if	if	SCONJ
american_scientific_journal-7486	61	7	and	and	CCONJ
american_scientific_journal-7486	61	8	only	only	ADV
american_scientific_journal-7486	61	9	if	if	SCONJ
american_scientific_journal-7486	61	10	x	x	SYM
american_scientific_journal-7486	61	11	≡	≡	PROPN
american_scientific_journal-7486	61	12	5(mod	5(mod	NOUN
american_scientific_journal-7486	61	13	6	6	NUM
american_scientific_journal-7486	61	14	)	)	PUNCT
american_scientific_journal-7486	61	15	.	.	PUNCT
american_scientific_journal-7486	62	1	thus	thus	ADV
american_scientific_journal-7486	62	2	,	,	PUNCT
american_scientific_journal-7486	62	3	in	in	ADP
american_scientific_journal-7486	62	4	view	view	NOUN
american_scientific_journal-7486	62	5	of	of	ADP
american_scientific_journal-7486	62	6	(	(	PUNCT
american_scientific_journal-7486	62	7	2.2.1	2.2.1	NUM
american_scientific_journal-7486	62	8	)	)	PUNCT
american_scientific_journal-7486	62	9	and	and	CCONJ
american_scientific_journal-7486	62	10	(	(	PUNCT
american_scientific_journal-7486	62	11	2.2.2	2.2.2	NUM
american_scientific_journal-7486	62	12	)	)	PUNCT
american_scientific_journal-7486	62	13	,	,	PUNCT
american_scientific_journal-7486	62	14	our	our	PRON
american_scientific_journal-7486	62	15	assertion	assertion	NOUN
american_scientific_journal-7486	62	16	is	be	AUX
american_scientific_journal-7486	62	17	proved	prove	VERB
american_scientific_journal-7486	62	18	.	.	PUNCT
american_scientific_journal-7486	63	1	3	3	X
american_scientific_journal-7486	63	2	.	.	X
american_scientific_journal-7486	63	3	illustrations	illustration	NOUN
american_scientific_journal-7486	63	4	3.1	3.1	NUM
american_scientific_journal-7486	63	5	example	example	NOUN
american_scientific_journal-7486	63	6	let	let	VERB
american_scientific_journal-7486	63	7	us	we	PRON
american_scientific_journal-7486	63	8	check	check	VERB
american_scientific_journal-7486	63	9	whether	whether	SCONJ
american_scientific_journal-7486	63	10	280	280	NUM
american_scientific_journal-7486	63	11	is	be	AUX
american_scientific_journal-7486	63	12	prime	prime	ADJ
american_scientific_journal-7486	63	13	or	or	CCONJ
american_scientific_journal-7486	63	14	not	not	PART
american_scientific_journal-7486	63	15	.	.	PUNCT
american_scientific_journal-7486	64	1	the	the	DET
american_scientific_journal-7486	64	2	nearest	near	ADJ
american_scientific_journal-7486	64	3	multiple	multiple	NOUN
american_scientific_journal-7486	64	4	of	of	ADP
american_scientific_journal-7486	64	5	90	90	NUM
american_scientific_journal-7486	64	6	to	to	PART
american_scientific_journal-7486	64	7	280	280	NUM
american_scientific_journal-7486	64	8	is	be	AUX
american_scientific_journal-7486	64	9	270	270	NUM
american_scientific_journal-7486	64	10	.	.	PUNCT
american_scientific_journal-7486	65	1	therefore	therefore	ADV
american_scientific_journal-7486	65	2	x	x	X
american_scientific_journal-7486	65	3	−	−	PROPN
american_scientific_journal-7486	65	4	n90	n90	PROPN
american_scientific_journal-7486	65	5	−	−	PROPN
american_scientific_journal-7486	65	6	5	5	NUM
american_scientific_journal-7486	65	7	=	=	SYM
american_scientific_journal-7486	65	8	5	5	NUM
american_scientific_journal-7486	65	9	,	,	PUNCT
american_scientific_journal-7486	65	10	and	and	CCONJ
american_scientific_journal-7486	65	11	5	5	NUM
american_scientific_journal-7486	65	12	is	be	AUX
american_scientific_journal-7486	65	13	not	not	PART
american_scientific_journal-7486	65	14	exactly	exactly	ADV
american_scientific_journal-7486	65	15	divisible	divisible	ADJ
american_scientific_journal-7486	65	16	by	by	ADP
american_scientific_journal-7486	65	17	6	6	NUM
american_scientific_journal-7486	65	18	.	.	PUNCT
american_scientific_journal-7486	66	1	now	now	ADV
american_scientific_journal-7486	66	2	checking	check	VERB
american_scientific_journal-7486	66	3	the	the	DET
american_scientific_journal-7486	66	4	other	other	ADJ
american_scientific_journal-7486	66	5	possibility	possibility	NOUN
american_scientific_journal-7486	66	6	,	,	PUNCT
american_scientific_journal-7486	66	7	i.e.	i.e.	X
american_scientific_journal-7486	66	8	,	,	PUNCT
american_scientific_journal-7486	66	9	x	x	PUNCT
american_scientific_journal-7486	66	10	−	−	PROPN
american_scientific_journal-7486	66	11	n90	n90	NOUN
american_scientific_journal-7486	66	12	−	−	PROPN
american_scientific_journal-7486	66	13	7	7	NUM
american_scientific_journal-7486	66	14	=	=	SYM
american_scientific_journal-7486	66	15	3	3	NUM
american_scientific_journal-7486	66	16	,	,	PUNCT
american_scientific_journal-7486	66	17	and	and	CCONJ
american_scientific_journal-7486	66	18	3	3	NUM
american_scientific_journal-7486	66	19	is	be	AUX
american_scientific_journal-7486	66	20	not	not	PART
american_scientific_journal-7486	66	21	divisible	divisible	ADJ
american_scientific_journal-7486	66	22	by	by	ADP
american_scientific_journal-7486	66	23	6	6	NUM
american_scientific_journal-7486	66	24	.	.	PUNCT
american_scientific_journal-7486	67	1	thus	thus	ADV
american_scientific_journal-7486	67	2	,	,	PUNCT
american_scientific_journal-7486	67	3	we	we	PRON
american_scientific_journal-7486	67	4	conclude	conclude	VERB
american_scientific_journal-7486	67	5	that	that	SCONJ
american_scientific_journal-7486	67	6	280	280	NUM
american_scientific_journal-7486	67	7	is	be	AUX
american_scientific_journal-7486	67	8	not	not	PART
american_scientific_journal-7486	67	9	a	a	DET
american_scientific_journal-7486	67	10	prime	prime	ADJ
american_scientific_journal-7486	67	11	number	number	NOUN
american_scientific_journal-7486	67	12	.	.	PUNCT
american_scientific_journal-7486	68	1	3.2	3.2	NUM
american_scientific_journal-7486	68	2	example	example	NOUN
american_scientific_journal-7486	68	3	let	let	VERB
american_scientific_journal-7486	68	4	us	we	PRON
american_scientific_journal-7486	68	5	check	check	VERB
american_scientific_journal-7486	68	6	whether	whether	SCONJ
american_scientific_journal-7486	68	7	397	397	NUM
american_scientific_journal-7486	68	8	is	be	AUX
american_scientific_journal-7486	68	9	prime	prime	ADJ
american_scientific_journal-7486	68	10	or	or	CCONJ
american_scientific_journal-7486	68	11	not	not	PART
american_scientific_journal-7486	68	12	.	.	PUNCT
american_scientific_journal-7486	69	1	the	the	DET
american_scientific_journal-7486	69	2	nearest	near	ADJ
american_scientific_journal-7486	69	3	multiple	multiple	NOUN
american_scientific_journal-7486	69	4	of	of	ADP
american_scientific_journal-7486	69	5	90	90	NUM
american_scientific_journal-7486	69	6	to	to	PART
american_scientific_journal-7486	69	7	397	397	NUM
american_scientific_journal-7486	69	8	is	be	AUX
american_scientific_journal-7486	69	9	360	360	NUM
american_scientific_journal-7486	69	10	.	.	PUNCT
american_scientific_journal-7486	70	1	therefore	therefore	ADV
american_scientific_journal-7486	70	2	x	x	X
american_scientific_journal-7486	70	3	−	−	PROPN
american_scientific_journal-7486	70	4	n90	n90	PROPN
american_scientific_journal-7486	70	5	−	−	PROPN
american_scientific_journal-7486	70	6	5	5	NUM
american_scientific_journal-7486	70	7	=	=	SYM
american_scientific_journal-7486	70	8	32	32	NUM
american_scientific_journal-7486	70	9	,	,	PUNCT
american_scientific_journal-7486	70	10	and	and	CCONJ
american_scientific_journal-7486	70	11	32	32	NUM
american_scientific_journal-7486	70	12	is	be	AUX
american_scientific_journal-7486	70	13	not	not	PART
american_scientific_journal-7486	70	14	exactly	exactly	ADV
american_scientific_journal-7486	70	15	divisible	divisible	ADJ
american_scientific_journal-7486	70	16	by	by	ADP
american_scientific_journal-7486	70	17	6	6	NUM
american_scientific_journal-7486	70	18	.	.	PUNCT
american_scientific_journal-7486	71	1	american	american	ADJ
american_scientific_journal-7486	71	2	academic	academic	ADJ
american_scientific_journal-7486	71	3	scientific	scientific	ADJ
american_scientific_journal-7486	71	4	research	research	NOUN
american_scientific_journal-7486	71	5	journal	journal	NOUN
american_scientific_journal-7486	71	6	for	for	ADP
american_scientific_journal-7486	71	7	engineering	engineering	NOUN
american_scientific_journal-7486	71	8	,	,	PUNCT
american_scientific_journal-7486	71	9	technology	technology	NOUN
american_scientific_journal-7486	71	10	,	,	PUNCT
american_scientific_journal-7486	71	11	and	and	CCONJ
american_scientific_journal-7486	71	12	sciences	science	NOUN
american_scientific_journal-7486	71	13	(	(	PUNCT
american_scientific_journal-7486	71	14	asrjets	asrjet	NOUN
american_scientific_journal-7486	71	15	)	)	PUNCT
american_scientific_journal-7486	71	16	(	(	PUNCT
american_scientific_journal-7486	71	17	2022	2022	NUM
american_scientific_journal-7486	71	18	)	)	PUNCT
american_scientific_journal-7486	71	19	volume	volume	NOUN
american_scientific_journal-7486	71	20	88	88	NUM
american_scientific_journal-7486	71	21	,	,	PUNCT
american_scientific_journal-7486	71	22	no	no	DET
american_scientific_journal-7486	71	23	1	1	NUM
american_scientific_journal-7486	71	24	,	,	PUNCT
american_scientific_journal-7486	71	25	pp	pp	ADV
american_scientific_journal-7486	71	26	77	77	NUM
american_scientific_journal-7486	71	27	-	-	SYM
american_scientific_journal-7486	71	28	90	90	NUM
american_scientific_journal-7486	71	29	81	81	NUM
american_scientific_journal-7486	71	30	now	now	ADV
american_scientific_journal-7486	71	31	checking	check	VERB
american_scientific_journal-7486	71	32	the	the	DET
american_scientific_journal-7486	71	33	other	other	ADJ
american_scientific_journal-7486	71	34	possibility	possibility	NOUN
american_scientific_journal-7486	71	35	,	,	PUNCT
american_scientific_journal-7486	71	36	i.e.	i.e.	X
american_scientific_journal-7486	71	37	,	,	PUNCT
american_scientific_journal-7486	71	38	x	x	PUNCT
american_scientific_journal-7486	71	39	−	−	PROPN
american_scientific_journal-7486	71	40	n90	n90	PROPN
american_scientific_journal-7486	71	41	−7	−7	NOUN
american_scientific_journal-7486	71	42	=	=	SYM
american_scientific_journal-7486	71	43	30	30	NUM
american_scientific_journal-7486	71	44	,	,	PUNCT
american_scientific_journal-7486	71	45	and	and	CCONJ
american_scientific_journal-7486	71	46	30	30	NUM
american_scientific_journal-7486	71	47	is	be	AUX
american_scientific_journal-7486	71	48	divisible	divisible	ADJ
american_scientific_journal-7486	71	49	by	by	ADP
american_scientific_journal-7486	71	50	6	6	NUM
american_scientific_journal-7486	71	51	.	.	PUNCT
american_scientific_journal-7486	72	1	thus	thus	ADV
american_scientific_journal-7486	72	2	,	,	PUNCT
american_scientific_journal-7486	72	3	we	we	PRON
american_scientific_journal-7486	72	4	conclude	conclude	VERB
american_scientific_journal-7486	72	5	that	that	SCONJ
american_scientific_journal-7486	72	6	397	397	NUM
american_scientific_journal-7486	72	7	is	be	AUX
american_scientific_journal-7486	72	8	a	a	DET
american_scientific_journal-7486	72	9	strong	strong	ADJ
american_scientific_journal-7486	72	10	probable	probable	ADJ
american_scientific_journal-7486	72	11	prime	prime	ADJ
american_scientific_journal-7486	72	12	number	number	NOUN
american_scientific_journal-7486	72	13	,	,	PUNCT
american_scientific_journal-7486	72	14	which	which	PRON
american_scientific_journal-7486	72	15	in	in	ADP
american_scientific_journal-7486	72	16	this	this	DET
american_scientific_journal-7486	72	17	case	case	NOUN
american_scientific_journal-7486	72	18	is	be	AUX
american_scientific_journal-7486	72	19	a	a	DET
american_scientific_journal-7486	72	20	prime	prime	ADJ
american_scientific_journal-7486	72	21	number	number	NOUN
american_scientific_journal-7486	72	22	.	.	PUNCT
american_scientific_journal-7486	73	1	3.3	3.3	NUM
american_scientific_journal-7486	73	2	remark	remark	NOUN
american_scientific_journal-7486	73	3	.	.	PUNCT
american_scientific_journal-7486	74	1	it	it	PRON
american_scientific_journal-7486	74	2	is	be	AUX
american_scientific_journal-7486	74	3	to	to	PART
american_scientific_journal-7486	74	4	be	be	AUX
american_scientific_journal-7486	74	5	noted	note	VERB
american_scientific_journal-7486	74	6	that	that	SCONJ
american_scientific_journal-7486	74	7	one	one	PRON
american_scientific_journal-7486	74	8	can	can	AUX
american_scientific_journal-7486	74	9	also	also	ADV
american_scientific_journal-7486	74	10	check	check	VERB
american_scientific_journal-7486	74	11	these	these	DET
american_scientific_journal-7486	74	12	two	two	NUM
american_scientific_journal-7486	74	13	examples	example	NOUN
american_scientific_journal-7486	74	14	with	with	ADP
american_scientific_journal-7486	74	15	the	the	DET
american_scientific_journal-7486	74	16	matlab	matlab	PROPN
american_scientific_journal-7486	74	17	code	code	NOUN
american_scientific_journal-7486	74	18	given	give	VERB
american_scientific_journal-7486	74	19	in	in	ADP
american_scientific_journal-7486	74	20	appendix	appendix	NOUN
american_scientific_journal-7486	74	21	1	1	NUM
american_scientific_journal-7486	74	22	.	.	NOUN
american_scientific_journal-7486	74	23	4	4	NUM
american_scientific_journal-7486	74	24	.	.	X
american_scientific_journal-7486	74	25	connection	connection	NOUN
american_scientific_journal-7486	74	26	between	between	ADP
american_scientific_journal-7486	74	27	the	the	DET
american_scientific_journal-7486	74	28	collatz	collatz	NOUN
american_scientific_journal-7486	74	29	conjecture	conjecture	NOUN
american_scientific_journal-7486	74	30	and	and	CCONJ
american_scientific_journal-7486	74	31	prime	prime	ADJ
american_scientific_journal-7486	74	32	numbers	number	NOUN
american_scientific_journal-7486	74	33	the	the	DET
american_scientific_journal-7486	74	34	collatz	collatz	NOUN
american_scientific_journal-7486	74	35	conjecture	conjecture	NOUN
american_scientific_journal-7486	74	36	is	be	AUX
american_scientific_journal-7486	74	37	named	name	VERB
american_scientific_journal-7486	74	38	after	after	ADP
american_scientific_journal-7486	74	39	a	a	DET
american_scientific_journal-7486	74	40	mathematician	mathematician	ADJ
american_scientific_journal-7486	74	41	lothar	lothar	PROPN
american_scientific_journal-7486	74	42	collatz	collatz	PROPN
american_scientific_journal-7486	74	43	who	who	PRON
american_scientific_journal-7486	74	44	wrote	write	VERB
american_scientific_journal-7486	74	45	the	the	DET
american_scientific_journal-7486	74	46	conjecture	conjecture	NOUN
american_scientific_journal-7486	74	47	in	in	ADP
american_scientific_journal-7486	74	48	1937	1937	NUM
american_scientific_journal-7486	74	49	.	.	PUNCT
american_scientific_journal-7486	75	1	it	it	PRON
american_scientific_journal-7486	75	2	is	be	AUX
american_scientific_journal-7486	75	3	also	also	ADV
american_scientific_journal-7486	75	4	known	know	VERB
american_scientific_journal-7486	75	5	as	as	ADP
american_scientific_journal-7486	75	6	the	the	DET
american_scientific_journal-7486	75	7	3n	3n	NUM
american_scientific_journal-7486	75	8	+	+	CCONJ
american_scientific_journal-7486	75	9	1	1	NUM
american_scientific_journal-7486	75	10	conjecture	conjecture	NOUN
american_scientific_journal-7486	75	11	.	.	PUNCT
american_scientific_journal-7486	76	1	the	the	DET
american_scientific_journal-7486	76	2	collatz	collatz	PROPN
american_scientific_journal-7486	76	3	conjecture	conjecture	VERB
american_scientific_journal-7486	76	4	states	state	VERB
american_scientific_journal-7486	76	5	the	the	DET
american_scientific_journal-7486	76	6	following	follow	VERB
american_scientific_journal-7486	76	7	consider	consider	VERB
american_scientific_journal-7486	76	8	a	a	DET
american_scientific_journal-7486	76	9	number	number	NOUN
american_scientific_journal-7486	76	10	x	x	NOUN
american_scientific_journal-7486	76	11	,	,	PUNCT
american_scientific_journal-7486	76	12	if	if	SCONJ
american_scientific_journal-7486	76	13	the	the	DET
american_scientific_journal-7486	76	14	number	number	NOUN
american_scientific_journal-7486	76	15	x	x	PUNCT
american_scientific_journal-7486	76	16	is	be	AUX
american_scientific_journal-7486	76	17	even	even	ADV
american_scientific_journal-7486	76	18	,	,	PUNCT
american_scientific_journal-7486	76	19	divide	divide	VERB
american_scientific_journal-7486	76	20	it	it	PRON
american_scientific_journal-7486	76	21	by	by	ADP
american_scientific_journal-7486	76	22	2	2	NUM
american_scientific_journal-7486	76	23	.	.	PUNCT
american_scientific_journal-7486	77	1	if	if	SCONJ
american_scientific_journal-7486	77	2	the	the	DET
american_scientific_journal-7486	77	3	number	number	NOUN
american_scientific_journal-7486	77	4	x	x	PUNCT
american_scientific_journal-7486	77	5	is	be	AUX
american_scientific_journal-7486	77	6	odd	odd	ADJ
american_scientific_journal-7486	77	7	,	,	PUNCT
american_scientific_journal-7486	77	8	triple	triple	ADJ
american_scientific_journal-7486	77	9	it	it	PRON
american_scientific_journal-7486	77	10	and	and	CCONJ
american_scientific_journal-7486	77	11	add	add	VERB
american_scientific_journal-7486	77	12	one	one	NUM
american_scientific_journal-7486	77	13	.	.	PUNCT
american_scientific_journal-7486	78	1	further	far	ADV
american_scientific_journal-7486	78	2	,	,	PUNCT
american_scientific_journal-7486	78	3	it	it	PRON
american_scientific_journal-7486	78	4	states	state	VERB
american_scientific_journal-7486	78	5	that	that	SCONJ
american_scientific_journal-7486	78	6	regardless	regardless	ADV
american_scientific_journal-7486	78	7	of	of	ADP
american_scientific_journal-7486	78	8	the	the	DET
american_scientific_journal-7486	78	9	choice	choice	NOUN
american_scientific_journal-7486	78	10	of	of	ADP
american_scientific_journal-7486	78	11	x	x	PRON
american_scientific_journal-7486	78	12	,	,	PUNCT
american_scientific_journal-7486	78	13	after	after	SCONJ
american_scientific_journal-7486	78	14	some	some	DET
american_scientific_journal-7486	78	15	iterations	iteration	NOUN
american_scientific_journal-7486	78	16	of	of	ADP
american_scientific_journal-7486	78	17	the	the	DET
american_scientific_journal-7486	78	18	collatz	collatz	NOUN
american_scientific_journal-7486	78	19	conjecture	conjecture	VERB
american_scientific_journal-7486	78	20	,	,	PUNCT
american_scientific_journal-7486	78	21	the	the	DET
american_scientific_journal-7486	78	22	number	number	NOUN
american_scientific_journal-7486	78	23	x	x	PRON
american_scientific_journal-7486	78	24	reaches	reach	VERB
american_scientific_journal-7486	78	25	1	1	NUM
american_scientific_journal-7486	78	26	.	.	PUNCT
american_scientific_journal-7486	78	27	before	before	ADP
american_scientific_journal-7486	78	28	proceeding	proceed	VERB
american_scientific_journal-7486	78	29	further	far	ADV
american_scientific_journal-7486	78	30	,	,	PUNCT
american_scientific_journal-7486	78	31	we	we	PRON
american_scientific_journal-7486	78	32	set	set	VERB
american_scientific_journal-7486	78	33	a	a	DET
american_scientific_journal-7486	78	34	name	name	NOUN
american_scientific_journal-7486	78	35	for	for	ADP
american_scientific_journal-7486	78	36	a	a	DET
american_scientific_journal-7486	78	37	number	number	NOUN
american_scientific_journal-7486	78	38	whence	whence	NOUN
american_scientific_journal-7486	78	39	applied	apply	VERB
american_scientific_journal-7486	78	40	the	the	DET
american_scientific_journal-7486	78	41	collatz	collatz	NOUN
american_scientific_journal-7486	78	42	conjecture	conjecture	NOUN
american_scientific_journal-7486	78	43	on	on	ADP
american_scientific_journal-7486	78	44	it	it	PRON
american_scientific_journal-7486	78	45	.	.	PUNCT
american_scientific_journal-7486	79	1	4.1	4.1	NUM
american_scientific_journal-7486	79	2	definition	definition	NOUN
american_scientific_journal-7486	79	3	[	[	X
american_scientific_journal-7486	79	4	see	see	VERB
american_scientific_journal-7486	79	5	8	8	NUM
american_scientific_journal-7486	79	6	and	and	CCONJ
american_scientific_journal-7486	79	7	9	9	NUM
american_scientific_journal-7486	79	8	]	]	X
american_scientific_journal-7486	79	9	let	let	VERB
american_scientific_journal-7486	79	10	x	x	PRON
american_scientific_journal-7486	79	11	be	be	AUX
american_scientific_journal-7486	79	12	a	a	DET
american_scientific_journal-7486	79	13	number	number	NOUN
american_scientific_journal-7486	79	14	,	,	PUNCT
american_scientific_journal-7486	79	15	then	then	ADV
american_scientific_journal-7486	79	16	we	we	PRON
american_scientific_journal-7486	79	17	say	say	VERB
american_scientific_journal-7486	79	18	y	y	PROPN
american_scientific_journal-7486	79	19	as	as	ADP
american_scientific_journal-7486	79	20	a	a	DET
american_scientific_journal-7486	79	21	collatz	collatz	NOUN
american_scientific_journal-7486	79	22	number	number	NOUN
american_scientific_journal-7486	79	23	of	of	ADP
american_scientific_journal-7486	79	24	x	x	PUNCT
american_scientific_journal-7486	79	25	defined	define	VERB
american_scientific_journal-7486	79	26	as	as	ADP
american_scientific_journal-7486	79	27	:	:	PUNCT
american_scientific_journal-7486	79	28	•	•	ADP
american_scientific_journal-7486	79	29	if	if	SCONJ
american_scientific_journal-7486	79	30	x	x	PRON
american_scientific_journal-7486	79	31	is	be	AUX
american_scientific_journal-7486	79	32	even	even	ADV
american_scientific_journal-7486	79	33	,	,	PUNCT
american_scientific_journal-7486	79	34	then	then	ADV
american_scientific_journal-7486	79	35	y	y	PROPN
american_scientific_journal-7486	79	36	=	=	PUNCT
american_scientific_journal-7486	80	1	x	x	PROPN
american_scientific_journal-7486	80	2	/2	/2	NUM
american_scientific_journal-7486	81	1	•	•	INTJ
american_scientific_journal-7486	81	2	if	if	SCONJ
american_scientific_journal-7486	81	3	x	x	PRON
american_scientific_journal-7486	81	4	is	be	AUX
american_scientific_journal-7486	81	5	odd	odd	ADJ
american_scientific_journal-7486	81	6	,	,	PUNCT
american_scientific_journal-7486	81	7	then	then	ADV
american_scientific_journal-7486	81	8	y	y	PROPN
american_scientific_journal-7486	81	9	=	=	PUNCT
american_scientific_journal-7486	82	1	3x	3x	PROPN
american_scientific_journal-7486	83	1	+	+	NOUN
american_scientific_journal-7486	83	2	1	1	X
american_scientific_journal-7486	83	3	.	.	PUNCT
american_scientific_journal-7486	83	4	now	now	ADV
american_scientific_journal-7486	83	5	using	use	VERB
american_scientific_journal-7486	83	6	the	the	DET
american_scientific_journal-7486	83	7	collatz	collatz	NOUN
american_scientific_journal-7486	83	8	conjecture	conjecture	NOUN
american_scientific_journal-7486	83	9	and	and	CCONJ
american_scientific_journal-7486	83	10	the	the	DET
american_scientific_journal-7486	83	11	previous	previous	ADJ
american_scientific_journal-7486	83	12	theorem	theorem	NOUN
american_scientific_journal-7486	83	13	,	,	PUNCT
american_scientific_journal-7486	83	14	we	we	PRON
american_scientific_journal-7486	83	15	have	have	VERB
american_scientific_journal-7486	83	16	the	the	DET
american_scientific_journal-7486	83	17	following	follow	VERB
american_scientific_journal-7486	83	18	theorem	theorem	VERB
american_scientific_journal-7486	83	19	.	.	PROPN
american_scientific_journal-7486	84	1	4.2	4.2	NUM
american_scientific_journal-7486	84	2	theorem	theorem	NOUN
american_scientific_journal-7486	84	3	let	let	VERB
american_scientific_journal-7486	84	4	x	x	PRON
american_scientific_journal-7486	84	5	be	be	AUX
american_scientific_journal-7486	84	6	an	an	DET
american_scientific_journal-7486	84	7	even	even	ADJ
american_scientific_journal-7486	84	8	number	number	NOUN
american_scientific_journal-7486	84	9	and	and	CCONJ
american_scientific_journal-7486	84	10	x	x	NOUN
american_scientific_journal-7486	84	11	is	be	AUX
american_scientific_journal-7486	84	12	not	not	PART
american_scientific_journal-7486	84	13	a	a	DET
american_scientific_journal-7486	84	14	multiple	multiple	NOUN
american_scientific_journal-7486	84	15	of	of	ADP
american_scientific_journal-7486	84	16	6	6	NUM
american_scientific_journal-7486	84	17	,	,	PUNCT
american_scientific_journal-7486	84	18	then	then	ADV
american_scientific_journal-7486	84	19	every	every	DET
american_scientific_journal-7486	84	20	prime	prime	ADJ
american_scientific_journal-7486	84	21	number	number	NOUN
american_scientific_journal-7486	84	22	except	except	SCONJ
american_scientific_journal-7486	84	23	3	3	NUM
american_scientific_journal-7486	84	24	is	be	AUX
american_scientific_journal-7486	84	25	a	a	DET
american_scientific_journal-7486	84	26	collatz	collatz	NOUN
american_scientific_journal-7486	84	27	number	number	NOUN
american_scientific_journal-7486	84	28	of	of	ADP
american_scientific_journal-7486	84	29	some	some	DET
american_scientific_journal-7486	84	30	x.	x.	NOUN
american_scientific_journal-7486	84	31	4.3	4.3	NUM
american_scientific_journal-7486	84	32	proof	proof	NOUN
american_scientific_journal-7486	84	33	to	to	PART
american_scientific_journal-7486	84	34	prove	prove	VERB
american_scientific_journal-7486	84	35	this	this	DET
american_scientific_journal-7486	84	36	theorem	theorem	NOUN
american_scientific_journal-7486	84	37	,	,	PUNCT
american_scientific_journal-7486	84	38	we	we	PRON
american_scientific_journal-7486	84	39	construct	construct	VERB
american_scientific_journal-7486	84	40	a	a	DET
american_scientific_journal-7486	84	41	three	three	NUM
american_scientific_journal-7486	84	42	column	column	NOUN
american_scientific_journal-7486	84	43	structure	structure	NOUN
american_scientific_journal-7486	84	44	of	of	ADP
american_scientific_journal-7486	84	45	numbers	number	NOUN
american_scientific_journal-7486	84	46	which	which	PRON
american_scientific_journal-7486	84	47	will	will	AUX
american_scientific_journal-7486	84	48	help	help	VERB
american_scientific_journal-7486	84	49	us	we	PRON
american_scientific_journal-7486	84	50	in	in	ADP
american_scientific_journal-7486	84	51	predicting	predict	VERB
american_scientific_journal-7486	84	52	a	a	DET
american_scientific_journal-7486	84	53	strong	strong	ADJ
american_scientific_journal-7486	84	54	candidate	candidate	NOUN
american_scientific_journal-7486	84	55	for	for	ADP
american_scientific_journal-7486	84	56	prime	prime	ADJ
american_scientific_journal-7486	84	57	numbers	number	NOUN
american_scientific_journal-7486	84	58	.	.	PUNCT
american_scientific_journal-7486	85	1	the	the	DET
american_scientific_journal-7486	85	2	three	three	NUM
american_scientific_journal-7486	85	3	column	column	NOUN
american_scientific_journal-7486	85	4	structure	structure	NOUN
american_scientific_journal-7486	85	5	is	be	AUX
american_scientific_journal-7486	85	6	explained	explain	VERB
american_scientific_journal-7486	85	7	in	in	ADP
american_scientific_journal-7486	85	8	figure	figure	NOUN
american_scientific_journal-7486	85	9	1	1	NUM
american_scientific_journal-7486	85	10	.	.	PUNCT
american_scientific_journal-7486	86	1	let	let	VERB
american_scientific_journal-7486	86	2	x	x	PRON
american_scientific_journal-7486	86	3	be	be	AUX
american_scientific_journal-7486	86	4	a	a	DET
american_scientific_journal-7486	86	5	given	give	VERB
american_scientific_journal-7486	86	6	number	number	NOUN
american_scientific_journal-7486	86	7	and	and	CCONJ
american_scientific_journal-7486	86	8	n90	n90	PROPN
american_scientific_journal-7486	86	9	be	be	AUX
american_scientific_journal-7486	86	10	the	the	DET
american_scientific_journal-7486	86	11	multiple	multiple	NOUN
american_scientific_journal-7486	86	12	of	of	ADP
american_scientific_journal-7486	86	13	90	90	NUM
american_scientific_journal-7486	86	14	nearest	near	ADJ
american_scientific_journal-7486	86	15	to	to	PART
american_scientific_journal-7486	86	16	x.	x.	VERB
american_scientific_journal-7486	86	17	now	now	ADV
american_scientific_journal-7486	86	18	if	if	SCONJ
american_scientific_journal-7486	86	19	x	x	PUNCT
american_scientific_journal-7486	86	20	−	−	PROPN
american_scientific_journal-7486	86	21	n90	n90	NOUN
american_scientific_journal-7486	86	22	−	−	PROPN
american_scientific_journal-7486	86	23	7	7	NUM
american_scientific_journal-7486	86	24	or	or	CCONJ
american_scientific_journal-7486	86	25	x	x	SYM
american_scientific_journal-7486	86	26	−	−	PROPN
american_scientific_journal-7486	86	27	n90	n90	PROPN
american_scientific_journal-7486	86	28	−	−	PROPN
american_scientific_journal-7486	86	29	5	5	NUM
american_scientific_journal-7486	86	30	is	be	AUX
american_scientific_journal-7486	86	31	divisible	divisible	ADJ
american_scientific_journal-7486	86	32	by	by	ADP
american_scientific_journal-7486	86	33	6	6	NUM
american_scientific_journal-7486	86	34	,	,	PUNCT
american_scientific_journal-7486	86	35	then	then	ADV
american_scientific_journal-7486	86	36	we	we	PRON
american_scientific_journal-7486	86	37	know	know	VERB
american_scientific_journal-7486	86	38	from	from	ADP
american_scientific_journal-7486	86	39	the	the	DET
american_scientific_journal-7486	86	40	previous	previous	ADJ
american_scientific_journal-7486	86	41	theorem	theorem	NOUN
american_scientific_journal-7486	86	42	that	that	PRON
american_scientific_journal-7486	86	43	x	x	PRON
american_scientific_journal-7486	86	44	is	be	AUX
american_scientific_journal-7486	86	45	a	a	DET
american_scientific_journal-7486	86	46	strong	strong	ADJ
american_scientific_journal-7486	86	47	american	american	ADJ
american_scientific_journal-7486	86	48	academic	academic	ADJ
american_scientific_journal-7486	86	49	scientific	scientific	ADJ
american_scientific_journal-7486	86	50	research	research	NOUN
american_scientific_journal-7486	86	51	journal	journal	NOUN
american_scientific_journal-7486	86	52	for	for	ADP
american_scientific_journal-7486	86	53	engineering	engineering	NOUN
american_scientific_journal-7486	86	54	,	,	PUNCT
american_scientific_journal-7486	86	55	technology	technology	NOUN
american_scientific_journal-7486	86	56	,	,	PUNCT
american_scientific_journal-7486	86	57	and	and	CCONJ
american_scientific_journal-7486	86	58	sciences	science	NOUN
american_scientific_journal-7486	86	59	(	(	PUNCT
american_scientific_journal-7486	86	60	asrjets	asrjet	NOUN
american_scientific_journal-7486	86	61	)	)	PUNCT
american_scientific_journal-7486	86	62	(	(	PUNCT
american_scientific_journal-7486	86	63	2022	2022	NUM
american_scientific_journal-7486	86	64	)	)	PUNCT
american_scientific_journal-7486	86	65	volume	volume	NOUN
american_scientific_journal-7486	86	66	88	88	NUM
american_scientific_journal-7486	86	67	,	,	PUNCT
american_scientific_journal-7486	86	68	no	no	DET
american_scientific_journal-7486	86	69	1	1	NUM
american_scientific_journal-7486	86	70	,	,	PUNCT
american_scientific_journal-7486	86	71	pp	pp	ADV
american_scientific_journal-7486	86	72	77	77	NUM
american_scientific_journal-7486	86	73	-	-	SYM
american_scientific_journal-7486	86	74	90	90	NUM
american_scientific_journal-7486	86	75	82	82	NUM
american_scientific_journal-7486	86	76	candidate	candidate	NOUN
american_scientific_journal-7486	86	77	for	for	ADP
american_scientific_journal-7486	86	78	prime	prime	ADJ
american_scientific_journal-7486	86	79	number	number	NOUN
american_scientific_journal-7486	86	80	.	.	PUNCT
american_scientific_journal-7486	87	1	in	in	ADP
american_scientific_journal-7486	87	2	these	these	DET
american_scientific_journal-7486	87	3	two	two	NUM
american_scientific_journal-7486	87	4	cases	case	NOUN
american_scientific_journal-7486	87	5	,	,	PUNCT
american_scientific_journal-7486	87	6	we	we	PRON
american_scientific_journal-7486	87	7	will	will	AUX
american_scientific_journal-7486	87	8	allocate	allocate	VERB
american_scientific_journal-7486	87	9	x	x	X
american_scientific_journal-7486	87	10	to	to	ADP
american_scientific_journal-7486	87	11	column	column	NOUN
american_scientific_journal-7486	87	12	1	1	NUM
american_scientific_journal-7486	87	13	(	(	PUNCT
american_scientific_journal-7486	87	14	c1	c1	PROPN
american_scientific_journal-7486	87	15	)	)	PUNCT
american_scientific_journal-7486	87	16	and	and	CCONJ
american_scientific_journal-7486	87	17	column	column	NOUN
american_scientific_journal-7486	87	18	2	2	NUM
american_scientific_journal-7486	87	19	(	(	PUNCT
american_scientific_journal-7486	87	20	c2	c2	PROPN
american_scientific_journal-7486	87	21	)	)	PUNCT
american_scientific_journal-7486	87	22	,	,	PUNCT
american_scientific_journal-7486	87	23	respectively	respectively	ADV
american_scientific_journal-7486	87	24	.	.	PUNCT
american_scientific_journal-7486	88	1	else	else	ADV
american_scientific_journal-7486	88	2	if	if	SCONJ
american_scientific_journal-7486	88	3	neither	neither	PRON
american_scientific_journal-7486	88	4	of	of	ADP
american_scientific_journal-7486	88	5	these	these	DET
american_scientific_journal-7486	88	6	two	two	NUM
american_scientific_journal-7486	88	7	things	thing	NOUN
american_scientific_journal-7486	88	8	happen	happen	VERB
american_scientific_journal-7486	88	9	,	,	PUNCT
american_scientific_journal-7486	88	10	then	then	ADV
american_scientific_journal-7486	88	11	from	from	ADP
american_scientific_journal-7486	88	12	the	the	DET
american_scientific_journal-7486	88	13	previous	previous	ADJ
american_scientific_journal-7486	88	14	theorem	theorem	NOUN
american_scientific_journal-7486	88	15	,	,	PUNCT
american_scientific_journal-7486	88	16	we	we	PRON
american_scientific_journal-7486	88	17	again	again	ADV
american_scientific_journal-7486	88	18	know	know	VERB
american_scientific_journal-7486	88	19	that	that	SCONJ
american_scientific_journal-7486	88	20	x	x	PRON
american_scientific_journal-7486	88	21	is	be	AUX
american_scientific_journal-7486	88	22	not	not	PART
american_scientific_journal-7486	88	23	a	a	DET
american_scientific_journal-7486	88	24	prime	prime	ADJ
american_scientific_journal-7486	88	25	number	number	NOUN
american_scientific_journal-7486	88	26	and	and	CCONJ
american_scientific_journal-7486	88	27	we	we	PRON
american_scientific_journal-7486	88	28	allocate	allocate	VERB
american_scientific_journal-7486	88	29	x	x	VERB
american_scientific_journal-7486	88	30	to	to	ADP
american_scientific_journal-7486	88	31	column	column	NOUN
american_scientific_journal-7486	88	32	3	3	NUM
american_scientific_journal-7486	88	33	(	(	PUNCT
american_scientific_journal-7486	88	34	c3	c3	PROPN
american_scientific_journal-7486	88	35	)	)	PUNCT
american_scientific_journal-7486	88	36	.	.	PUNCT
american_scientific_journal-7486	89	1	from	from	ADP
american_scientific_journal-7486	89	2	the	the	DET
american_scientific_journal-7486	89	3	three	three	NUM
american_scientific_journal-7486	89	4	column	column	NOUN
american_scientific_journal-7486	89	5	structure	structure	NOUN
american_scientific_journal-7486	89	6	in	in	ADP
american_scientific_journal-7486	89	7	figure	figure	NOUN
american_scientific_journal-7486	89	8	1	1	NUM
american_scientific_journal-7486	89	9	below	below	ADV
american_scientific_journal-7486	89	10	,	,	PUNCT
american_scientific_journal-7486	89	11	we	we	PRON
american_scientific_journal-7486	89	12	observe	observe	VERB
american_scientific_journal-7486	89	13	all	all	DET
american_scientific_journal-7486	89	14	the	the	DET
american_scientific_journal-7486	89	15	primes	prime	NOUN
american_scientific_journal-7486	89	16	except	except	SCONJ
american_scientific_journal-7486	89	17	3	3	NUM
american_scientific_journal-7486	89	18	lie	lie	NOUN
american_scientific_journal-7486	89	19	in	in	ADP
american_scientific_journal-7486	89	20	c1	c1	PROPN
american_scientific_journal-7486	89	21	or	or	CCONJ
american_scientific_journal-7486	89	22	c2	c2	PROPN
american_scientific_journal-7486	89	23	only	only	ADV
american_scientific_journal-7486	89	24	.	.	PUNCT
american_scientific_journal-7486	90	1	thus	thus	ADV
american_scientific_journal-7486	90	2	the	the	DET
american_scientific_journal-7486	90	3	number	number	NOUN
american_scientific_journal-7486	90	4	arrangement	arrangement	NOUN
american_scientific_journal-7486	90	5	in	in	ADP
american_scientific_journal-7486	90	6	our	our	PRON
american_scientific_journal-7486	90	7	three	three	NUM
american_scientific_journal-7486	90	8	column	column	NOUN
american_scientific_journal-7486	90	9	set	set	NOUN
american_scientific_journal-7486	90	10	-	-	PUNCT
american_scientific_journal-7486	90	11	up	up	NOUN
american_scientific_journal-7486	90	12	is	be	AUX
american_scientific_journal-7486	90	13	as	as	ADP
american_scientific_journal-7486	90	14	the	the	DET
american_scientific_journal-7486	90	15	following	following	NOUN
american_scientific_journal-7486	90	16	:	:	PUNCT
american_scientific_journal-7486	90	17	figure	figure	NOUN
american_scientific_journal-7486	90	18	1	1	NUM
american_scientific_journal-7486	90	19	:	:	PUNCT
american_scientific_journal-7486	90	20	three	three	NUM
american_scientific_journal-7486	90	21	column	column	NOUN
american_scientific_journal-7486	90	22	structure	structure	NOUN
american_scientific_journal-7486	90	23	.	.	PUNCT
american_scientific_journal-7486	91	1	where	where	SCONJ
american_scientific_journal-7486	91	2	t	t	PROPN
american_scientific_journal-7486	91	3	is	be	AUX
american_scientific_journal-7486	91	4	the	the	DET
american_scientific_journal-7486	91	5	transpose	transpose	NOUN
american_scientific_journal-7486	91	6	of	of	ADP
american_scientific_journal-7486	91	7	the	the	DET
american_scientific_journal-7486	91	8	array	array	NOUN
american_scientific_journal-7486	91	9	.	.	PUNCT
american_scientific_journal-7486	92	1	case	case	NOUN
american_scientific_journal-7486	92	2	studies	study	NOUN
american_scientific_journal-7486	92	3	.	.	PUNCT
american_scientific_journal-7486	93	1	american	american	ADJ
american_scientific_journal-7486	93	2	academic	academic	ADJ
american_scientific_journal-7486	93	3	scientific	scientific	ADJ
american_scientific_journal-7486	93	4	research	research	NOUN
american_scientific_journal-7486	93	5	journal	journal	NOUN
american_scientific_journal-7486	93	6	for	for	ADP
american_scientific_journal-7486	93	7	engineering	engineering	NOUN
american_scientific_journal-7486	93	8	,	,	PUNCT
american_scientific_journal-7486	93	9	technology	technology	NOUN
american_scientific_journal-7486	93	10	,	,	PUNCT
american_scientific_journal-7486	93	11	and	and	CCONJ
american_scientific_journal-7486	93	12	sciences	science	NOUN
american_scientific_journal-7486	93	13	(	(	PUNCT
american_scientific_journal-7486	93	14	asrjets	asrjet	NOUN
american_scientific_journal-7486	93	15	)	)	PUNCT
american_scientific_journal-7486	93	16	(	(	PUNCT
american_scientific_journal-7486	93	17	2022	2022	NUM
american_scientific_journal-7486	93	18	)	)	PUNCT
american_scientific_journal-7486	93	19	volume	volume	NOUN
american_scientific_journal-7486	93	20	88	88	NUM
american_scientific_journal-7486	93	21	,	,	PUNCT
american_scientific_journal-7486	93	22	no	no	DET
american_scientific_journal-7486	93	23	1	1	NUM
american_scientific_journal-7486	93	24	,	,	PUNCT
american_scientific_journal-7486	93	25	pp	pp	ADV
american_scientific_journal-7486	93	26	77	77	NUM
american_scientific_journal-7486	93	27	-	-	SYM
american_scientific_journal-7486	93	28	90	90	NUM
american_scientific_journal-7486	93	29	83	83	NUM
american_scientific_journal-7486	93	30	now	now	ADV
american_scientific_journal-7486	93	31	let	let	VERB
american_scientific_journal-7486	93	32	’s	’s	NOUN
american_scientific_journal-7486	93	33	consider	consider	VERB
american_scientific_journal-7486	93	34	the	the	DET
american_scientific_journal-7486	93	35	collatz	collatz	NOUN
american_scientific_journal-7486	93	36	number	number	NOUN
american_scientific_journal-7486	93	37	of	of	ADP
american_scientific_journal-7486	93	38	a	a	DET
american_scientific_journal-7486	93	39	given	give	VERB
american_scientific_journal-7486	93	40	number	number	NOUN
american_scientific_journal-7486	93	41	.	.	PUNCT
american_scientific_journal-7486	94	1	y	y	NOUN
american_scientific_journal-7486	94	2	=	=	PUNCT
american_scientific_journal-7486	95	1	x	x	PROPN
american_scientific_journal-7486	95	2	/2	/2	NOUN
american_scientific_journal-7486	96	1	if	if	SCONJ
american_scientific_journal-7486	96	2	x	x	PRON
american_scientific_journal-7486	96	3	is	be	AUX
american_scientific_journal-7486	96	4	even	even	ADV
american_scientific_journal-7486	96	5	and	and	CCONJ
american_scientific_journal-7486	96	6	y	y	PROPN
american_scientific_journal-7486	96	7	=	=	PUNCT
american_scientific_journal-7486	97	1	3x	3x	PROPN
american_scientific_journal-7486	98	1	+	+	CCONJ
american_scientific_journal-7486	98	2	1	1	NUM
american_scientific_journal-7486	98	3	if	if	SCONJ
american_scientific_journal-7486	98	4	x	x	PRON
american_scientific_journal-7486	98	5	is	be	AUX
american_scientific_journal-7486	98	6	odd	odd	ADJ
american_scientific_journal-7486	98	7	.	.	PUNCT
american_scientific_journal-7486	99	1	(	(	PUNCT
american_scientific_journal-7486	99	2	4.1	4.1	NUM
american_scientific_journal-7486	99	3	)	)	PUNCT
american_scientific_journal-7486	99	4	we	we	PRON
american_scientific_journal-7486	99	5	will	will	AUX
american_scientific_journal-7486	99	6	discuss	discuss	VERB
american_scientific_journal-7486	99	7	the	the	DET
american_scientific_journal-7486	99	8	possibility	possibility	NOUN
american_scientific_journal-7486	99	9	of	of	ADP
american_scientific_journal-7486	99	10	odd	odd	ADJ
american_scientific_journal-7486	99	11	x	x	NOUN
american_scientific_journal-7486	99	12	’s	’s	NOUN
american_scientific_journal-7486	99	13	in	in	ADP
american_scientific_journal-7486	99	14	two	two	NUM
american_scientific_journal-7486	99	15	cases	case	NOUN
american_scientific_journal-7486	99	16	:	:	PUNCT
american_scientific_journal-7486	99	17	case	case	NOUN
american_scientific_journal-7486	99	18	1	1	NUM
american_scientific_journal-7486	99	19	if	if	SCONJ
american_scientific_journal-7486	99	20	x	x	PRON
american_scientific_journal-7486	99	21	is	be	AUX
american_scientific_journal-7486	99	22	odd	odd	ADJ
american_scientific_journal-7486	99	23	,	,	PUNCT
american_scientific_journal-7486	99	24	then	then	ADV
american_scientific_journal-7486	99	25	in	in	ADP
american_scientific_journal-7486	99	26	the	the	DET
american_scientific_journal-7486	99	27	collatz	collatz	NOUN
american_scientific_journal-7486	99	28	number	number	NOUN
american_scientific_journal-7486	99	29	y	y	PROPN
american_scientific_journal-7486	99	30	of	of	ADP
american_scientific_journal-7486	99	31	x	x	PRON
american_scientific_journal-7486	99	32	,	,	PUNCT
american_scientific_journal-7486	99	33	we	we	PRON
american_scientific_journal-7486	99	34	have	have	VERB
american_scientific_journal-7486	99	35	two	two	NUM
american_scientific_journal-7486	99	36	operations	operation	NOUN
american_scientific_journal-7486	99	37	,	,	PUNCT
american_scientific_journal-7486	99	38	magnification	magnification	NOUN
american_scientific_journal-7486	99	39	by	by	ADP
american_scientific_journal-7486	99	40	3	3	NUM
american_scientific_journal-7486	99	41	and	and	CCONJ
american_scientific_journal-7486	99	42	then	then	ADV
american_scientific_journal-7486	99	43	translation	translation	NOUN
american_scientific_journal-7486	99	44	by	by	ADP
american_scientific_journal-7486	99	45	one	one	NUM
american_scientific_journal-7486	99	46	.	.	PUNCT
american_scientific_journal-7486	100	1	thus	thus	ADV
american_scientific_journal-7486	100	2	we	we	PRON
american_scientific_journal-7486	100	3	observe	observe	VERB
american_scientific_journal-7486	100	4	that	that	SCONJ
american_scientific_journal-7486	100	5	every	every	DET
american_scientific_journal-7486	100	6	odd	odd	ADJ
american_scientific_journal-7486	100	7	x	x	VERB
american_scientific_journal-7486	100	8	is	be	AUX
american_scientific_journal-7486	100	9	firstly	firstly	ADV
american_scientific_journal-7486	100	10	projected	project	VERB
american_scientific_journal-7486	100	11	to	to	ADP
american_scientific_journal-7486	100	12	c3	c3	PROPN
american_scientific_journal-7486	100	13	by	by	ADP
american_scientific_journal-7486	100	14	the	the	DET
american_scientific_journal-7486	100	15	multiplication	multiplication	NOUN
american_scientific_journal-7486	100	16	of	of	ADP
american_scientific_journal-7486	100	17	3	3	NUM
american_scientific_journal-7486	100	18	,	,	PUNCT
american_scientific_journal-7486	100	19	but	but	CCONJ
american_scientific_journal-7486	100	20	when	when	SCONJ
american_scientific_journal-7486	100	21	translated	translate	VERB
american_scientific_journal-7486	100	22	by	by	ADP
american_scientific_journal-7486	100	23	unity	unity	NOUN
american_scientific_journal-7486	100	24	,	,	PUNCT
american_scientific_journal-7486	100	25	it	it	PRON
american_scientific_journal-7486	100	26	is	be	AUX
american_scientific_journal-7486	100	27	projected	project	VERB
american_scientific_journal-7486	100	28	back	back	ADV
american_scientific_journal-7486	100	29	to	to	ADP
american_scientific_journal-7486	100	30	c1	c1	PROPN
american_scientific_journal-7486	100	31	.	.	PUNCT
american_scientific_journal-7486	101	1	now	now	ADV
american_scientific_journal-7486	101	2	,	,	PUNCT
american_scientific_journal-7486	101	3	we	we	PRON
american_scientific_journal-7486	101	4	again	again	ADV
american_scientific_journal-7486	101	5	look	look	VERB
american_scientific_journal-7486	101	6	at	at	ADP
american_scientific_journal-7486	101	7	the	the	DET
american_scientific_journal-7486	101	8	operation	operation	NOUN
american_scientific_journal-7486	101	9	on	on	ADP
american_scientific_journal-7486	101	10	odd	odd	ADJ
american_scientific_journal-7486	101	11	x.	x.	NOUN
american_scientific_journal-7486	101	12	the	the	DET
american_scientific_journal-7486	101	13	number	number	NOUN
american_scientific_journal-7486	101	14	3	3	NUM
american_scientific_journal-7486	101	15	is	be	AUX
american_scientific_journal-7486	101	16	odd	odd	ADJ
american_scientific_journal-7486	101	17	,	,	PUNCT
american_scientific_journal-7486	101	18	x	x	PUNCT
american_scientific_journal-7486	101	19	is	be	AUX
american_scientific_journal-7486	101	20	odd	odd	ADJ
american_scientific_journal-7486	101	21	,	,	PUNCT
american_scientific_journal-7486	101	22	and	and	CCONJ
american_scientific_journal-7486	101	23	so	so	ADV
american_scientific_journal-7486	101	24	3x	3x	PROPN
american_scientific_journal-7486	101	25	is	be	AUX
american_scientific_journal-7486	101	26	odd	odd	ADJ
american_scientific_journal-7486	101	27	.	.	PUNCT
american_scientific_journal-7486	102	1	when	when	SCONJ
american_scientific_journal-7486	102	2	we	we	PRON
american_scientific_journal-7486	102	3	add	add	VERB
american_scientific_journal-7486	102	4	up	up	ADP
american_scientific_journal-7486	102	5	one	one	NUM
american_scientific_journal-7486	102	6	to	to	ADP
american_scientific_journal-7486	102	7	3x	3x	NUM
american_scientific_journal-7486	102	8	,	,	PUNCT
american_scientific_journal-7486	102	9	the	the	DET
american_scientific_journal-7486	102	10	number	number	NOUN
american_scientific_journal-7486	102	11	3x	3x	NUM
american_scientific_journal-7486	102	12	+	+	CCONJ
american_scientific_journal-7486	102	13	1	1	NUM
american_scientific_journal-7486	102	14	=	=	SYM
american_scientific_journal-7486	102	15	y	y	PROPN
american_scientific_journal-7486	102	16	∈	∈	PROPN
american_scientific_journal-7486	102	17	c1	c1	PROPN
american_scientific_journal-7486	102	18	is	be	AUX
american_scientific_journal-7486	102	19	always	always	ADV
american_scientific_journal-7486	102	20	even	even	ADV
american_scientific_journal-7486	102	21	.	.	PUNCT
american_scientific_journal-7486	103	1	thus	thus	ADV
american_scientific_journal-7486	103	2	3x	3x	NUM
american_scientific_journal-7486	103	3	+	+	CCONJ
american_scientific_journal-7486	103	4	1	1	NUM
american_scientific_journal-7486	103	5	can	can	AUX
american_scientific_journal-7486	103	6	never	never	ADV
american_scientific_journal-7486	103	7	be	be	AUX
american_scientific_journal-7486	103	8	a	a	DET
american_scientific_journal-7486	103	9	possible	possible	ADJ
american_scientific_journal-7486	103	10	prime	prime	ADJ
american_scientific_journal-7486	103	11	number	number	NOUN
american_scientific_journal-7486	103	12	.	.	PUNCT
american_scientific_journal-7486	104	1	case	case	NOUN
american_scientific_journal-7486	104	2	2	2	NUM
american_scientific_journal-7486	104	3	if	if	SCONJ
american_scientific_journal-7486	104	4	x	x	PRON
american_scientific_journal-7486	104	5	is	be	AUX
american_scientific_journal-7486	104	6	even	even	ADV
american_scientific_journal-7486	104	7	,	,	PUNCT
american_scientific_journal-7486	104	8	then	then	ADV
american_scientific_journal-7486	104	9	the	the	DET
american_scientific_journal-7486	104	10	collatz	collatz	NOUN
american_scientific_journal-7486	104	11	number	number	NOUN
american_scientific_journal-7486	104	12	y	y	PROPN
american_scientific_journal-7486	105	1	=	=	PUNCT
american_scientific_journal-7486	105	2	x	x	X
american_scientific_journal-7486	105	3	/2	/2	PROPN
american_scientific_journal-7486	105	4	may	may	AUX
american_scientific_journal-7486	105	5	project	project	VERB
american_scientific_journal-7486	105	6	to	to	ADP
american_scientific_journal-7486	105	7	any	any	PRON
american_scientific_journal-7486	105	8	of	of	ADP
american_scientific_journal-7486	105	9	the	the	DET
american_scientific_journal-7486	105	10	three	three	NUM
american_scientific_journal-7486	105	11	columns	column	NOUN
american_scientific_journal-7486	105	12	c1	c1	NOUN
american_scientific_journal-7486	105	13	,	,	PUNCT
american_scientific_journal-7486	105	14	c2	c2	PROPN
american_scientific_journal-7486	105	15	or	or	CCONJ
american_scientific_journal-7486	105	16	c3	c3	PROPN
american_scientific_journal-7486	105	17	.	.	PUNCT
american_scientific_journal-7486	106	1	if	if	SCONJ
american_scientific_journal-7486	106	2	y	y	PROPN
american_scientific_journal-7486	106	3	goes	go	VERB
american_scientific_journal-7486	106	4	to	to	ADP
american_scientific_journal-7486	106	5	c1	c1	PROPN
american_scientific_journal-7486	106	6	or	or	CCONJ
american_scientific_journal-7486	106	7	c2	c2	PROPN
american_scientific_journal-7486	106	8	,	,	PUNCT
american_scientific_journal-7486	106	9	then	then	ADV
american_scientific_journal-7486	106	10	y	y	PROPN
american_scientific_journal-7486	106	11	is	be	AUX
american_scientific_journal-7486	106	12	a	a	DET
american_scientific_journal-7486	106	13	strong	strong	ADJ
american_scientific_journal-7486	106	14	candidate	candidate	NOUN
american_scientific_journal-7486	106	15	for	for	ADP
american_scientific_journal-7486	106	16	a	a	DET
american_scientific_journal-7486	106	17	prime	prime	ADJ
american_scientific_journal-7486	106	18	number	number	NOUN
american_scientific_journal-7486	106	19	.	.	PUNCT
american_scientific_journal-7486	107	1	if	if	SCONJ
american_scientific_journal-7486	107	2	y	y	PROPN
american_scientific_journal-7486	107	3	is	be	AUX
american_scientific_journal-7486	107	4	in	in	ADP
american_scientific_journal-7486	107	5	c3	c3	PROPN
american_scientific_journal-7486	107	6	,	,	PUNCT
american_scientific_journal-7486	107	7	then	then	ADV
american_scientific_journal-7486	107	8	y	y	PROPN
american_scientific_journal-7486	107	9	is	be	AUX
american_scientific_journal-7486	107	10	never	never	ADV
american_scientific_journal-7486	107	11	a	a	DET
american_scientific_journal-7486	107	12	prime	prime	ADJ
american_scientific_journal-7486	107	13	number	number	NOUN
american_scientific_journal-7486	107	14	.	.	PUNCT
american_scientific_journal-7486	108	1	so	so	ADV
american_scientific_journal-7486	108	2	we	we	PRON
american_scientific_journal-7486	108	3	exclude	exclude	VERB
american_scientific_journal-7486	108	4	the	the	DET
american_scientific_journal-7486	108	5	choices	choice	NOUN
american_scientific_journal-7486	108	6	for	for	SCONJ
american_scientific_journal-7486	108	7	y	y	PROPN
american_scientific_journal-7486	108	8	to	to	PART
american_scientific_journal-7486	108	9	sit	sit	VERB
american_scientific_journal-7486	108	10	in	in	ADP
american_scientific_journal-7486	108	11	c3	c3	PROPN
american_scientific_journal-7486	108	12	.	.	PUNCT
american_scientific_journal-7486	109	1	it	it	PRON
american_scientific_journal-7486	109	2	is	be	AUX
american_scientific_journal-7486	109	3	straightforward	straightforward	ADJ
american_scientific_journal-7486	109	4	to	to	PART
american_scientific_journal-7486	109	5	see	see	VERB
american_scientific_journal-7486	109	6	that	that	SCONJ
american_scientific_journal-7486	109	7	the	the	DET
american_scientific_journal-7486	109	8	numbers	number	NOUN
american_scientific_journal-7486	109	9	of	of	ADP
american_scientific_journal-7486	109	10	c3	c3	PROPN
american_scientific_journal-7486	109	11	are	be	AUX
american_scientific_journal-7486	109	12	the	the	DET
american_scientific_journal-7486	109	13	multiples	multiple	NOUN
american_scientific_journal-7486	109	14	of	of	ADP
american_scientific_journal-7486	109	15	3	3	NUM
american_scientific_journal-7486	109	16	.	.	PUNCT
american_scientific_journal-7486	110	1	in	in	ADP
american_scientific_journal-7486	110	2	other	other	ADJ
american_scientific_journal-7486	110	3	words	word	NOUN
american_scientific_journal-7486	110	4	,	,	PUNCT
american_scientific_journal-7486	110	5	we	we	PRON
american_scientific_journal-7486	110	6	can	can	AUX
american_scientific_journal-7486	110	7	say	say	VERB
american_scientific_journal-7486	110	8	that	that	SCONJ
american_scientific_journal-7486	110	9	the	the	DET
american_scientific_journal-7486	110	10	even	even	ADV
american_scientific_journal-7486	110	11	x	x	PRON
american_scientific_journal-7486	110	12	should	should	AUX
american_scientific_journal-7486	110	13	not	not	PART
american_scientific_journal-7486	110	14	be	be	AUX
american_scientific_journal-7486	110	15	a	a	DET
american_scientific_journal-7486	110	16	multiple	multiple	NOUN
american_scientific_journal-7486	110	17	of	of	ADP
american_scientific_journal-7486	110	18	6	6	NUM
american_scientific_journal-7486	110	19	.	.	PUNCT
american_scientific_journal-7486	111	1	on	on	ADP
american_scientific_journal-7486	111	2	excluding	exclude	VERB
american_scientific_journal-7486	111	3	the	the	DET
american_scientific_journal-7486	111	4	even	even	ADJ
american_scientific_journal-7486	111	5	numbers	number	NOUN
american_scientific_journal-7486	111	6	which	which	PRON
american_scientific_journal-7486	111	7	are	be	AUX
american_scientific_journal-7486	111	8	multiples	multiple	NOUN
american_scientific_journal-7486	111	9	of	of	ADP
american_scientific_journal-7486	111	10	6	6	NUM
american_scientific_journal-7486	111	11	,	,	PUNCT
american_scientific_journal-7486	111	12	the	the	DET
american_scientific_journal-7486	111	13	corresponding	corresponding	ADJ
american_scientific_journal-7486	111	14	collatz	collatz	NOUN
american_scientific_journal-7486	111	15	numbers	number	NOUN
american_scientific_journal-7486	111	16	is	be	AUX
american_scientific_journal-7486	111	17	a	a	DET
american_scientific_journal-7486	111	18	strong	strong	ADJ
american_scientific_journal-7486	111	19	prime	prime	ADJ
american_scientific_journal-7486	111	20	candidate	candidate	NOUN
american_scientific_journal-7486	111	21	.	.	PUNCT
american_scientific_journal-7486	112	1	this	this	PRON
american_scientific_journal-7486	112	2	proves	prove	VERB
american_scientific_journal-7486	112	3	the	the	DET
american_scientific_journal-7486	112	4	result	result	NOUN
american_scientific_journal-7486	112	5	.	.	PUNCT
american_scientific_journal-7486	113	1	from	from	ADP
american_scientific_journal-7486	113	2	the	the	DET
american_scientific_journal-7486	113	3	above	above	ADJ
american_scientific_journal-7486	113	4	theorem	theorem	NOUN
american_scientific_journal-7486	113	5	,	,	PUNCT
american_scientific_journal-7486	113	6	we	we	PRON
american_scientific_journal-7486	113	7	can	can	AUX
american_scientific_journal-7486	113	8	easily	easily	ADV
american_scientific_journal-7486	113	9	state	state	VERB
american_scientific_journal-7486	113	10	the	the	DET
american_scientific_journal-7486	113	11	following	following	NOUN
american_scientific_journal-7486	113	12	.	.	PUNCT
american_scientific_journal-7486	114	1	4.4	4.4	NUM
american_scientific_journal-7486	114	2	.corollary	.corollary	NUM
american_scientific_journal-7486	114	3	every	every	DET
american_scientific_journal-7486	114	4	prime	prime	ADJ
american_scientific_journal-7486	114	5	number	number	NOUN
american_scientific_journal-7486	114	6	greater	great	ADJ
american_scientific_journal-7486	114	7	than	than	ADP
american_scientific_journal-7486	114	8	30	30	NUM
american_scientific_journal-7486	114	9	can	can	AUX
american_scientific_journal-7486	114	10	be	be	AUX
american_scientific_journal-7486	114	11	obtained	obtain	VERB
american_scientific_journal-7486	114	12	from	from	ADP
american_scientific_journal-7486	114	13	the	the	DET
american_scientific_journal-7486	114	14	sequence	sequence	NOUN
american_scientific_journal-7486	114	15	of	of	ADP
american_scientific_journal-7486	114	16	numbers	number	NOUN
american_scientific_journal-7486	114	17	:	:	PUNCT
american_scientific_journal-7486	114	18	n30	n30	PROPN
american_scientific_journal-7486	114	19	+	+	CCONJ
american_scientific_journal-7486	114	20	1	1	NUM
american_scientific_journal-7486	114	21	+	+	NUM
american_scientific_journal-7486	114	22	6	6	NUM
american_scientific_journal-7486	114	23	+	+	NUM
american_scientific_journal-7486	114	24	4	4	NUM
american_scientific_journal-7486	114	25	+	+	SYM
american_scientific_journal-7486	114	26	2	2	NUM
american_scientific_journal-7486	114	27	+	+	CCONJ
american_scientific_journal-7486	114	28	4	4	NUM
american_scientific_journal-7486	114	29	+	+	SYM
american_scientific_journal-7486	114	30	2	2	NUM
american_scientific_journal-7486	114	31	+	+	CCONJ
american_scientific_journal-7486	114	32	4	4	NUM
american_scientific_journal-7486	114	33	+	+	SYM
american_scientific_journal-7486	114	34	6	6	NUM
american_scientific_journal-7486	114	35	,	,	PUNCT
american_scientific_journal-7486	114	36	where	where	SCONJ
american_scientific_journal-7486	114	37	n30	n30	PROPN
american_scientific_journal-7486	114	38	is	be	AUX
american_scientific_journal-7486	114	39	the	the	DET
american_scientific_journal-7486	114	40	nearest	near	ADJ
american_scientific_journal-7486	114	41	multiple	multiple	NOUN
american_scientific_journal-7486	114	42	of	of	ADP
american_scientific_journal-7486	114	43	30	30	NUM
american_scientific_journal-7486	114	44	less	less	ADJ
american_scientific_journal-7486	114	45	than	than	ADP
american_scientific_journal-7486	114	46	the	the	DET
american_scientific_journal-7486	114	47	given	give	VERB
american_scientific_journal-7486	114	48	prime	prime	NOUN
american_scientific_journal-7486	114	49	and	and	CCONJ
american_scientific_journal-7486	114	50	is	be	AUX
american_scientific_journal-7486	114	51	a	a	DET
american_scientific_journal-7486	114	52	whole	whole	ADJ
american_scientific_journal-7486	114	53	number	number	NOUN
american_scientific_journal-7486	114	54	.	.	PUNCT
american_scientific_journal-7486	115	1	4.5	4.5	NUM
american_scientific_journal-7486	115	2	.	.	PUNCT
american_scientific_journal-7486	115	3	remark	remark	NOUN
american_scientific_journal-7486	115	4	from	from	ADP
american_scientific_journal-7486	115	5	the	the	DET
american_scientific_journal-7486	115	6	above	above	ADJ
american_scientific_journal-7486	115	7	corollary	corollary	NOUN
american_scientific_journal-7486	115	8	,	,	PUNCT
american_scientific_journal-7486	115	9	we	we	PRON
american_scientific_journal-7486	115	10	observe	observe	VERB
american_scientific_journal-7486	115	11	that	that	SCONJ
american_scientific_journal-7486	115	12	the	the	DET
american_scientific_journal-7486	115	13	sequence	sequence	NOUN
american_scientific_journal-7486	115	14	of	of	ADP
american_scientific_journal-7486	115	15	numbers	number	NOUN
american_scientific_journal-7486	115	16	lie	lie	VERB
american_scientific_journal-7486	115	17	in	in	ADP
american_scientific_journal-7486	115	18	column	column	NOUN
american_scientific_journal-7486	115	19	1	1	NUM
american_scientific_journal-7486	115	20	and	and	CCONJ
american_scientific_journal-7486	115	21	column	column	NOUN
american_scientific_journal-7486	115	22	2	2	NUM
american_scientific_journal-7486	115	23	only	only	ADV
american_scientific_journal-7486	115	24	,	,	PUNCT
american_scientific_journal-7486	115	25	so	so	ADV
american_scientific_journal-7486	115	26	they	they	PRON
american_scientific_journal-7486	115	27	american	american	ADJ
american_scientific_journal-7486	115	28	academic	academic	ADJ
american_scientific_journal-7486	115	29	scientific	scientific	ADJ
american_scientific_journal-7486	115	30	research	research	NOUN
american_scientific_journal-7486	115	31	journal	journal	NOUN
american_scientific_journal-7486	115	32	for	for	ADP
american_scientific_journal-7486	115	33	engineering	engineering	NOUN
american_scientific_journal-7486	115	34	,	,	PUNCT
american_scientific_journal-7486	115	35	technology	technology	NOUN
american_scientific_journal-7486	115	36	,	,	PUNCT
american_scientific_journal-7486	115	37	and	and	CCONJ
american_scientific_journal-7486	115	38	sciences	science	NOUN
american_scientific_journal-7486	115	39	(	(	PUNCT
american_scientific_journal-7486	115	40	asrjets	asrjet	NOUN
american_scientific_journal-7486	115	41	)	)	PUNCT
american_scientific_journal-7486	115	42	(	(	PUNCT
american_scientific_journal-7486	115	43	2022	2022	NUM
american_scientific_journal-7486	115	44	)	)	PUNCT
american_scientific_journal-7486	115	45	volume	volume	NOUN
american_scientific_journal-7486	115	46	88	88	NUM
american_scientific_journal-7486	115	47	,	,	PUNCT
american_scientific_journal-7486	115	48	no	no	DET
american_scientific_journal-7486	115	49	1	1	NUM
american_scientific_journal-7486	115	50	,	,	PUNCT
american_scientific_journal-7486	115	51	pp	pp	ADV
american_scientific_journal-7486	115	52	77	77	NUM
american_scientific_journal-7486	115	53	-	-	SYM
american_scientific_journal-7486	115	54	90	90	NUM
american_scientific_journal-7486	115	55	84	84	NUM
american_scientific_journal-7486	115	56	are	be	AUX
american_scientific_journal-7486	115	57	always	always	ADV
american_scientific_journal-7486	115	58	strong	strong	ADJ
american_scientific_journal-7486	115	59	prime	prime	ADJ
american_scientific_journal-7486	115	60	candidates	candidate	NOUN
american_scientific_journal-7486	115	61	,	,	PUNCT
american_scientific_journal-7486	115	62	and	and	CCONJ
american_scientific_journal-7486	115	63	at	at	ADP
american_scientific_journal-7486	115	64	the	the	DET
american_scientific_journal-7486	115	65	same	same	ADJ
american_scientific_journal-7486	115	66	time	time	NOUN
american_scientific_journal-7486	115	67	this	this	DET
american_scientific_journal-7486	115	68	sequence	sequence	NOUN
american_scientific_journal-7486	115	69	is	be	AUX
american_scientific_journal-7486	115	70	excluding	exclude	VERB
american_scientific_journal-7486	115	71	a	a	DET
american_scientific_journal-7486	115	72	lot	lot	NOUN
american_scientific_journal-7486	115	73	of	of	ADP
american_scientific_journal-7486	115	74	non	non	ADJ
american_scientific_journal-7486	115	75	-	-	ADJ
american_scientific_journal-7486	115	76	prime	prime	ADJ
american_scientific_journal-7486	115	77	numbers	number	NOUN
american_scientific_journal-7486	115	78	.	.	PUNCT
american_scientific_journal-7486	116	1	4.6	4.6	NUM
american_scientific_journal-7486	116	2	.	.	PUNCT
american_scientific_journal-7486	116	3	remark	remark	NOUN
american_scientific_journal-7486	116	4	let	let	VERB
american_scientific_journal-7486	116	5	us	we	PRON
american_scientific_journal-7486	116	6	start	start	VERB
american_scientific_journal-7486	116	7	with	with	ADP
american_scientific_journal-7486	116	8	few	few	ADJ
american_scientific_journal-7486	116	9	new	new	ADJ
american_scientific_journal-7486	116	10	notations	notation	NOUN
american_scientific_journal-7486	116	11	.	.	PUNCT
american_scientific_journal-7486	117	1	if	if	SCONJ
american_scientific_journal-7486	117	2	x	x	PRON
american_scientific_journal-7486	117	3	is	be	AUX
american_scientific_journal-7486	117	4	an	an	DET
american_scientific_journal-7486	117	5	even	even	ADV
american_scientific_journal-7486	117	6	or	or	CCONJ
american_scientific_journal-7486	117	7	an	an	DET
american_scientific_journal-7486	117	8	odd	odd	ADJ
american_scientific_journal-7486	117	9	number	number	NOUN
american_scientific_journal-7486	117	10	,	,	PUNCT
american_scientific_journal-7486	117	11	we	we	PRON
american_scientific_journal-7486	117	12	say	say	VERB
american_scientific_journal-7486	117	13	x	x	PUNCT
american_scientific_journal-7486	117	14	as	as	ADP
american_scientific_journal-7486	117	15	a	a	DET
american_scientific_journal-7486	117	16	weak	weak	ADJ
american_scientific_journal-7486	117	17	collatz	collatz	NOUN
american_scientific_journal-7486	117	18	even	even	ADV
american_scientific_journal-7486	117	19	(	(	PUNCT
american_scientific_journal-7486	117	20	or	or	CCONJ
american_scientific_journal-7486	117	21	odd	odd	ADJ
american_scientific_journal-7486	117	22	)	)	PUNCT
american_scientific_journal-7486	117	23	number	number	NOUN
american_scientific_journal-7486	117	24	.	.	PUNCT
american_scientific_journal-7486	118	1	if	if	SCONJ
american_scientific_journal-7486	118	2	the	the	DET
american_scientific_journal-7486	118	3	first	first	ADJ
american_scientific_journal-7486	118	4	iteration	iteration	NOUN
american_scientific_journal-7486	118	5	of	of	ADP
american_scientific_journal-7486	118	6	the	the	DET
american_scientific_journal-7486	118	7	collatz	collatz	NOUN
american_scientific_journal-7486	118	8	conjecture	conjecture	NOUN
american_scientific_journal-7486	118	9	is	be	AUX
american_scientific_journal-7486	118	10	odd	odd	ADJ
american_scientific_journal-7486	118	11	,	,	PUNCT
american_scientific_journal-7486	118	12	for	for	ADP
american_scientific_journal-7486	118	13	example	example	NOUN
american_scientific_journal-7486	118	14	,	,	PUNCT
american_scientific_journal-7486	118	15	let	let	VERB
american_scientific_journal-7486	118	16	x	x	SYM
american_scientific_journal-7486	118	17	=	=	SYM
american_scientific_journal-7486	118	18	70	70	NUM
american_scientific_journal-7486	118	19	,	,	PUNCT
american_scientific_journal-7486	118	20	then	then	ADV
american_scientific_journal-7486	118	21	the	the	DET
american_scientific_journal-7486	118	22	first	first	ADJ
american_scientific_journal-7486	118	23	iteration	iteration	NOUN
american_scientific_journal-7486	118	24	in	in	ADP
american_scientific_journal-7486	118	25	the	the	DET
american_scientific_journal-7486	118	26	collatz	collatz	NOUN
american_scientific_journal-7486	118	27	conjecture	conjecture	NOUN
american_scientific_journal-7486	118	28	is	be	AUX
american_scientific_journal-7486	118	29	35	35	NUM
american_scientific_journal-7486	118	30	.	.	PUNCT
american_scientific_journal-7486	119	1	thus	thus	ADV
american_scientific_journal-7486	119	2	we	we	PRON
american_scientific_journal-7486	119	3	call	call	VERB
american_scientific_journal-7486	119	4	70	70	NUM
american_scientific_journal-7486	119	5	a	a	DET
american_scientific_journal-7486	119	6	weak	weak	ADJ
american_scientific_journal-7486	119	7	collatz	collatz	NOUN
american_scientific_journal-7486	119	8	even	even	ADV
american_scientific_journal-7486	119	9	number	number	NOUN
american_scientific_journal-7486	119	10	.	.	PUNCT
american_scientific_journal-7486	120	1	otherwise	otherwise	ADV
american_scientific_journal-7486	120	2	,	,	PUNCT
american_scientific_journal-7486	120	3	if	if	SCONJ
american_scientific_journal-7486	120	4	x	x	PRON
american_scientific_journal-7486	120	5	has	have	VERB
american_scientific_journal-7486	120	6	more	more	ADJ
american_scientific_journal-7486	120	7	than	than	ADP
american_scientific_journal-7486	120	8	one	one	NUM
american_scientific_journal-7486	120	9	even	even	ADV
american_scientific_journal-7486	120	10	iterations	iteration	NOUN
american_scientific_journal-7486	120	11	,	,	PUNCT
american_scientific_journal-7486	120	12	we	we	PRON
american_scientific_journal-7486	120	13	say	say	VERB
american_scientific_journal-7486	120	14	x	x	PRON
american_scientific_journal-7486	120	15	is	be	AUX
american_scientific_journal-7486	120	16	a	a	DET
american_scientific_journal-7486	120	17	strong	strong	ADJ
american_scientific_journal-7486	120	18	collatz	collatz	NOUN
american_scientific_journal-7486	120	19	even	even	ADV
american_scientific_journal-7486	120	20	number	number	NOUN
american_scientific_journal-7486	120	21	.	.	PUNCT
american_scientific_journal-7486	121	1	for	for	ADP
american_scientific_journal-7486	121	2	example	example	NOUN
american_scientific_journal-7486	121	3	48	48	NUM
american_scientific_journal-7486	121	4	is	be	AUX
american_scientific_journal-7486	121	5	a	a	DET
american_scientific_journal-7486	121	6	strong	strong	ADJ
american_scientific_journal-7486	121	7	collatz	collatz	NOUN
american_scientific_journal-7486	121	8	even	even	ADV
american_scientific_journal-7486	121	9	number	number	NOUN
american_scientific_journal-7486	121	10	having	have	VERB
american_scientific_journal-7486	121	11	multiple	multiple	ADJ
american_scientific_journal-7486	121	12	iterations	iteration	NOUN
american_scientific_journal-7486	121	13	{	{	PUNCT
american_scientific_journal-7486	121	14	48	48	NUM
american_scientific_journal-7486	121	15	,	,	PUNCT
american_scientific_journal-7486	121	16	24	24	NUM
american_scientific_journal-7486	121	17	,	,	PUNCT
american_scientific_journal-7486	121	18	12	12	NUM
american_scientific_journal-7486	121	19	,	,	PUNCT
american_scientific_journal-7486	121	20	6	6	NUM
american_scientific_journal-7486	121	21	,	,	PUNCT
american_scientific_journal-7486	121	22	3	3	NUM
american_scientific_journal-7486	121	23	,	,	PUNCT
american_scientific_journal-7486	121	24	·	·	PUNCT
american_scientific_journal-7486	121	25	·	·	PUNCT
american_scientific_journal-7486	121	26	·	·	PUNCT
american_scientific_journal-7486	121	27	}	}	PUNCT
american_scientific_journal-7486	121	28	.	.	PUNCT
american_scientific_journal-7486	122	1	similarly	similarly	ADV
american_scientific_journal-7486	122	2	,	,	PUNCT
american_scientific_journal-7486	122	3	in	in	ADP
american_scientific_journal-7486	122	4	case	case	NOUN
american_scientific_journal-7486	122	5	of	of	ADP
american_scientific_journal-7486	122	6	prime	prime	ADJ
american_scientific_journal-7486	122	7	numbers	number	NOUN
american_scientific_journal-7486	122	8	,	,	PUNCT
american_scientific_journal-7486	122	9	we	we	PRON
american_scientific_journal-7486	122	10	call	call	VERB
american_scientific_journal-7486	122	11	a	a	DET
american_scientific_journal-7486	122	12	prime	prime	ADJ
american_scientific_journal-7486	122	13	number	number	NOUN
american_scientific_journal-7486	122	14	as	as	ADP
american_scientific_journal-7486	122	15	a	a	DET
american_scientific_journal-7486	122	16	weak	weak	ADJ
american_scientific_journal-7486	122	17	collatz	collatz	NOUN
american_scientific_journal-7486	122	18	prime	prime	ADJ
american_scientific_journal-7486	122	19	number	number	NOUN
american_scientific_journal-7486	122	20	if	if	SCONJ
american_scientific_journal-7486	122	21	its	its	PRON
american_scientific_journal-7486	122	22	first	first	ADJ
american_scientific_journal-7486	122	23	collatz	collatz	NOUN
american_scientific_journal-7486	122	24	iteration	iteration	NOUN
american_scientific_journal-7486	122	25	is	be	AUX
american_scientific_journal-7486	122	26	odd	odd	ADJ
american_scientific_journal-7486	122	27	.	.	PUNCT
american_scientific_journal-7486	123	1	otherwise	otherwise	ADV
american_scientific_journal-7486	123	2	,	,	PUNCT
american_scientific_journal-7486	123	3	we	we	PRON
american_scientific_journal-7486	123	4	call	call	VERB
american_scientific_journal-7486	123	5	it	it	PRON
american_scientific_journal-7486	123	6	by	by	ADP
american_scientific_journal-7486	123	7	strong	strong	ADJ
american_scientific_journal-7486	123	8	collatz	collatz	NOUN
american_scientific_journal-7486	123	9	prime	prime	ADJ
american_scientific_journal-7486	123	10	number	number	NOUN
american_scientific_journal-7486	123	11	.	.	PUNCT
american_scientific_journal-7486	124	1	from	from	ADP
american_scientific_journal-7486	124	2	the	the	DET
american_scientific_journal-7486	124	3	above	above	ADJ
american_scientific_journal-7486	124	4	discussions	discussion	NOUN
american_scientific_journal-7486	124	5	,	,	PUNCT
american_scientific_journal-7486	124	6	we	we	PRON
american_scientific_journal-7486	124	7	observe	observe	VERB
american_scientific_journal-7486	124	8	to	to	PART
american_scientific_journal-7486	124	9	reach	reach	VERB
american_scientific_journal-7486	124	10	the	the	DET
american_scientific_journal-7486	124	11	final	final	ADJ
american_scientific_journal-7486	124	12	{	{	PUNCT
american_scientific_journal-7486	124	13	4	4	NUM
american_scientific_journal-7486	124	14	,	,	PUNCT
american_scientific_journal-7486	124	15	2	2	NUM
american_scientific_journal-7486	124	16	,	,	PUNCT
american_scientific_journal-7486	124	17	1	1	NUM
american_scientific_journal-7486	124	18	}	}	PUNCT
american_scientific_journal-7486	124	19	loop	loop	NOUN
american_scientific_journal-7486	124	20	,	,	PUNCT
american_scientific_journal-7486	124	21	the	the	DET
american_scientific_journal-7486	124	22	hailstorm	hailstorm	NOUN
american_scientific_journal-7486	124	23	numbers	number	NOUN
american_scientific_journal-7486	124	24	are	be	AUX
american_scientific_journal-7486	124	25	eventually	eventually	ADV
american_scientific_journal-7486	124	26	projected	project	VERB
american_scientific_journal-7486	124	27	from	from	ADP
american_scientific_journal-7486	124	28	a	a	DET
american_scientific_journal-7486	124	29	strong	strong	ADJ
american_scientific_journal-7486	124	30	collatz	collatz	NOUN
american_scientific_journal-7486	124	31	prime	prime	ADJ
american_scientific_journal-7486	124	32	number	number	NOUN
american_scientific_journal-7486	124	33	to	to	ADP
american_scientific_journal-7486	124	34	a	a	DET
american_scientific_journal-7486	124	35	strong	strong	ADJ
american_scientific_journal-7486	124	36	collatz	collatz	NOUN
american_scientific_journal-7486	124	37	even	even	ADV
american_scientific_journal-7486	124	38	number	number	NOUN
american_scientific_journal-7486	124	39	and	and	CCONJ
american_scientific_journal-7486	124	40	then	then	ADV
american_scientific_journal-7486	124	41	finally	finally	ADV
american_scientific_journal-7486	124	42	to	to	PART
american_scientific_journal-7486	124	43	{	{	PUNCT
american_scientific_journal-7486	124	44	4	4	NUM
american_scientific_journal-7486	124	45	,	,	PUNCT
american_scientific_journal-7486	124	46	2	2	NUM
american_scientific_journal-7486	124	47	,	,	PUNCT
american_scientific_journal-7486	124	48	1	1	NUM
american_scientific_journal-7486	124	49	}	}	PUNCT
american_scientific_journal-7486	124	50	loop	loop	NOUN
american_scientific_journal-7486	124	51	.	.	PUNCT
american_scientific_journal-7486	125	1	5	5	X
american_scientific_journal-7486	125	2	.	.	X
american_scientific_journal-7486	125	3	conclusion	conclusion	NOUN
american_scientific_journal-7486	125	4	users	user	NOUN
american_scientific_journal-7486	125	5	of	of	ADP
american_scientific_journal-7486	125	6	theorem	theorem	ADJ
american_scientific_journal-7486	125	7	2.1	2.1	NUM
american_scientific_journal-7486	125	8	will	will	AUX
american_scientific_journal-7486	125	9	successfully	successfully	ADV
american_scientific_journal-7486	125	10	achieve	achieve	VERB
american_scientific_journal-7486	125	11	to	to	PART
american_scientific_journal-7486	125	12	bring	bring	VERB
american_scientific_journal-7486	125	13	about	about	ADP
american_scientific_journal-7486	125	14	a	a	DET
american_scientific_journal-7486	125	15	desired	desire	VERB
american_scientific_journal-7486	125	16	result	result	NOUN
american_scientific_journal-7486	125	17	enabling	enable	VERB
american_scientific_journal-7486	125	18	them	they	PRON
american_scientific_journal-7486	125	19	to	to	PART
american_scientific_journal-7486	125	20	identify	identify	VERB
american_scientific_journal-7486	125	21	candidate	candidate	NOUN
american_scientific_journal-7486	125	22	prime	prime	ADJ
american_scientific_journal-7486	125	23	numbers	number	NOUN
american_scientific_journal-7486	125	24	for	for	ADP
american_scientific_journal-7486	125	25	uses	use	NOUN
american_scientific_journal-7486	125	26	in	in	ADP
american_scientific_journal-7486	125	27	algorithms	algorithm	NOUN
american_scientific_journal-7486	125	28	,	,	PUNCT
american_scientific_journal-7486	125	29	computing	computing	NOUN
american_scientific_journal-7486	125	30	and	and	CCONJ
american_scientific_journal-7486	125	31	mathematics	mathematic	NOUN
american_scientific_journal-7486	125	32	.	.	PUNCT
american_scientific_journal-7486	126	1	we	we	PRON
american_scientific_journal-7486	126	2	have	have	AUX
american_scientific_journal-7486	126	3	written	write	VERB
american_scientific_journal-7486	126	4	a	a	DET
american_scientific_journal-7486	126	5	matlab	matlab	PROPN
american_scientific_journal-7486	126	6	code	code	NOUN
american_scientific_journal-7486	126	7	for	for	ADP
american_scientific_journal-7486	126	8	theorem	theorem	ADJ
american_scientific_journal-7486	126	9	2.1	2.1	NUM
american_scientific_journal-7486	126	10	given	give	VERB
american_scientific_journal-7486	126	11	in	in	ADP
american_scientific_journal-7486	126	12	appendix	appendix	NOUN
american_scientific_journal-7486	126	13	1	1	NUM
american_scientific_journal-7486	126	14	.	.	PUNCT
american_scientific_journal-7486	127	1	this	this	PRON
american_scientific_journal-7486	127	2	will	will	AUX
american_scientific_journal-7486	127	3	help	help	VERB
american_scientific_journal-7486	127	4	the	the	DET
american_scientific_journal-7486	127	5	reader	reader	NOUN
american_scientific_journal-7486	127	6	to	to	PART
american_scientific_journal-7486	127	7	easily	easily	ADV
american_scientific_journal-7486	127	8	check	check	VERB
american_scientific_journal-7486	127	9	whether	whether	SCONJ
american_scientific_journal-7486	127	10	a	a	DET
american_scientific_journal-7486	127	11	number	number	NOUN
american_scientific_journal-7486	127	12	is	be	AUX
american_scientific_journal-7486	127	13	a	a	DET
american_scientific_journal-7486	127	14	probable	probable	ADJ
american_scientific_journal-7486	127	15	prime	prime	ADJ
american_scientific_journal-7486	127	16	number	number	NOUN
american_scientific_journal-7486	127	17	or	or	CCONJ
american_scientific_journal-7486	127	18	not	not	PART
american_scientific_journal-7486	127	19	.	.	PUNCT
american_scientific_journal-7486	128	1	this	this	DET
american_scientific_journal-7486	128	2	theorem	theorem	NOUN
american_scientific_journal-7486	128	3	also	also	ADV
american_scientific_journal-7486	128	4	contributes	contribute	VERB
american_scientific_journal-7486	128	5	to	to	PART
american_scientific_journal-7486	128	6	determine	determine	VERB
american_scientific_journal-7486	128	7	the	the	DET
american_scientific_journal-7486	128	8	predictable	predictable	ADJ
american_scientific_journal-7486	128	9	nature	nature	NOUN
american_scientific_journal-7486	128	10	of	of	ADP
american_scientific_journal-7486	128	11	prime	prime	ADJ
american_scientific_journal-7486	128	12	numbers	number	NOUN
american_scientific_journal-7486	128	13	explained	explain	VERB
american_scientific_journal-7486	128	14	in	in	ADP
american_scientific_journal-7486	128	15	the	the	DET
american_scientific_journal-7486	128	16	3	3	NUM
american_scientific_journal-7486	128	17	column	column	NOUN
american_scientific_journal-7486	128	18	structure	structure	NOUN
american_scientific_journal-7486	128	19	(	(	PUNCT
american_scientific_journal-7486	128	20	figure	figure	NOUN
american_scientific_journal-7486	128	21	1	1	NUM
american_scientific_journal-7486	128	22	)	)	PUNCT
american_scientific_journal-7486	128	23	,	,	PUNCT
american_scientific_journal-7486	128	24	and	and	CCONJ
american_scientific_journal-7486	128	25	will	will	AUX
american_scientific_journal-7486	128	26	hopefully	hopefully	ADV
american_scientific_journal-7486	128	27	make	make	VERB
american_scientific_journal-7486	128	28	a	a	DET
american_scientific_journal-7486	128	29	contribution	contribution	NOUN
american_scientific_journal-7486	128	30	on	on	ADP
american_scientific_journal-7486	128	31	improving	improve	VERB
american_scientific_journal-7486	128	32	prime	prime	ADJ
american_scientific_journal-7486	128	33	numbers	number	NOUN
american_scientific_journal-7486	128	34	understanding	understanding	NOUN
american_scientific_journal-7486	128	35	as	as	ADP
american_scientific_journal-7486	128	36	building	build	VERB
american_scientific_journal-7486	128	37	blocks	block	NOUN
american_scientific_journal-7486	128	38	for	for	ADP
american_scientific_journal-7486	128	39	future	future	ADJ
american_scientific_journal-7486	128	40	research	research	NOUN
american_scientific_journal-7486	128	41	and	and	CCONJ
american_scientific_journal-7486	128	42	development	development	NOUN
american_scientific_journal-7486	128	43	in	in	ADP
american_scientific_journal-7486	128	44	number	number	NOUN
american_scientific_journal-7486	128	45	theory	theory	NOUN
american_scientific_journal-7486	128	46	and	and	CCONJ
american_scientific_journal-7486	128	47	computing	computing	NOUN
american_scientific_journal-7486	128	48	.	.	PUNCT
american_scientific_journal-7486	129	1	we	we	PRON
american_scientific_journal-7486	129	2	have	have	AUX
american_scientific_journal-7486	129	3	also	also	ADV
american_scientific_journal-7486	129	4	obtained	obtain	VERB
american_scientific_journal-7486	129	5	a	a	DET
american_scientific_journal-7486	129	6	beautiful	beautiful	ADJ
american_scientific_journal-7486	129	7	connection	connection	NOUN
american_scientific_journal-7486	129	8	of	of	ADP
american_scientific_journal-7486	129	9	prime	prime	ADJ
american_scientific_journal-7486	129	10	numbers	number	NOUN
american_scientific_journal-7486	129	11	with	with	ADP
american_scientific_journal-7486	129	12	the	the	DET
american_scientific_journal-7486	129	13	very	very	ADV
american_scientific_journal-7486	129	14	famous	famous	ADJ
american_scientific_journal-7486	129	15	collatz	collatz	NOUN
american_scientific_journal-7486	129	16	conjecture	conjecture	NOUN
american_scientific_journal-7486	129	17	with	with	ADP
american_scientific_journal-7486	129	18	theorem	theorem	ADJ
american_scientific_journal-7486	129	19	4.2	4.2	NUM
american_scientific_journal-7486	129	20	.	.	PUNCT
american_scientific_journal-7486	130	1	(	(	PUNCT
american_scientific_journal-7486	130	2	see	see	VERB
american_scientific_journal-7486	130	3	matlab	matlab	PROPN
american_scientific_journal-7486	130	4	code	code	NOUN
american_scientific_journal-7486	130	5	in	in	ADP
american_scientific_journal-7486	130	6	appendix	appendix	ADJ
american_scientific_journal-7486	130	7	2	2	NUM
american_scientific_journal-7486	130	8	)	)	PUNCT
american_scientific_journal-7486	130	9	corollary	corollary	NOUN
american_scientific_journal-7486	130	10	4.4	4.4	NUM
american_scientific_journal-7486	130	11	serves	serve	VERB
american_scientific_journal-7486	130	12	as	as	ADP
american_scientific_journal-7486	130	13	a	a	DET
american_scientific_journal-7486	130	14	more	more	ADV
american_scientific_journal-7486	130	15	condensed	condensed	ADJ
american_scientific_journal-7486	130	16	look	look	NOUN
american_scientific_journal-7486	130	17	at	at	ADP
american_scientific_journal-7486	130	18	the	the	DET
american_scientific_journal-7486	130	19	3	3	NUM
american_scientific_journal-7486	130	20	column	column	NOUN
american_scientific_journal-7486	130	21	structure	structure	NOUN
american_scientific_journal-7486	130	22	and	and	CCONJ
american_scientific_journal-7486	130	23	an	an	DET
american_scientific_journal-7486	130	24	attempt	attempt	NOUN
american_scientific_journal-7486	130	25	to	to	ADP
american_scientific_journal-7486	130	26	a	a	DET
american_scientific_journal-7486	130	27	building	building	NOUN
american_scientific_journal-7486	130	28	block	block	NOUN
american_scientific_journal-7486	130	29	for	for	ADP
american_scientific_journal-7486	130	30	further	further	ADJ
american_scientific_journal-7486	130	31	improvement	improvement	NOUN
american_scientific_journal-7486	130	32	to	to	PART
american_scientific_journal-7486	130	33	formulate	formulate	VERB
american_scientific_journal-7486	130	34	a	a	DET
american_scientific_journal-7486	130	35	formula	formula	NOUN
american_scientific_journal-7486	130	36	for	for	ADP
american_scientific_journal-7486	130	37	prime	prime	ADJ
american_scientific_journal-7486	130	38	numbers	number	NOUN
american_scientific_journal-7486	130	39	.	.	PUNCT
american_scientific_journal-7486	131	1	(	(	PUNCT
american_scientific_journal-7486	131	2	see	see	VERB
american_scientific_journal-7486	131	3	matlab	matlab	PROPN
american_scientific_journal-7486	131	4	code	code	NOUN
american_scientific_journal-7486	131	5	in	in	ADP
american_scientific_journal-7486	131	6	appendix	appendix	NOUN
american_scientific_journal-7486	131	7	3	3	NUM
american_scientific_journal-7486	131	8	)	)	PUNCT
american_scientific_journal-7486	131	9	the	the	DET
american_scientific_journal-7486	131	10	observations	observation	NOUN
american_scientific_journal-7486	131	11	from	from	ADP
american_scientific_journal-7486	131	12	this	this	DET
american_scientific_journal-7486	131	13	research	research	NOUN
american_scientific_journal-7486	131	14	through	through	ADP
american_scientific_journal-7486	131	15	the	the	DET
american_scientific_journal-7486	131	16	3	3	NUM
american_scientific_journal-7486	131	17	column	column	NOUN
american_scientific_journal-7486	131	18	structure	structure	NOUN
american_scientific_journal-7486	131	19	has	have	AUX
american_scientific_journal-7486	131	20	clearly	clearly	ADV
american_scientific_journal-7486	131	21	revealed	reveal	VERB
american_scientific_journal-7486	131	22	a	a	DET
american_scientific_journal-7486	131	23	pattern	pattern	NOUN
american_scientific_journal-7486	131	24	for	for	ADP
american_scientific_journal-7486	131	25	the	the	DET
american_scientific_journal-7486	131	26	research	research	NOUN
american_scientific_journal-7486	131	27	on	on	ADP
american_scientific_journal-7486	131	28	prime	prime	ADJ
american_scientific_journal-7486	131	29	numbers	number	NOUN
american_scientific_journal-7486	131	30	and	and	CCONJ
american_scientific_journal-7486	131	31	their	their	PRON
american_scientific_journal-7486	131	32	predicted	predict	VERB
american_scientific_journal-7486	131	33	behavior	behavior	NOUN
american_scientific_journal-7486	131	34	.	.	PUNCT
american_scientific_journal-7486	132	1	theorem	theorem	VERB
american_scientific_journal-7486	132	2	2.1	2.1	NUM
american_scientific_journal-7486	132	3	“	"	PUNCT
american_scientific_journal-7486	132	4	every	every	DET
american_scientific_journal-7486	132	5	prime	prime	ADJ
american_scientific_journal-7486	132	6	number	number	NOUN
american_scientific_journal-7486	132	7	other	other	ADJ
american_scientific_journal-7486	132	8	than	than	ADP
american_scientific_journal-7486	132	9	2	2	NUM
american_scientific_journal-7486	132	10	and	and	CCONJ
american_scientific_journal-7486	132	11	3	3	NUM
american_scientific_journal-7486	132	12	satisfies	satisfie	NOUN
american_scientific_journal-7486	132	13	one	one	NUM
american_scientific_journal-7486	132	14	of	of	ADP
american_scientific_journal-7486	132	15	the	the	DET
american_scientific_journal-7486	132	16	following	follow	VERB
american_scientific_journal-7486	132	17	two	two	NUM
american_scientific_journal-7486	132	18	algebraic	algebraic	ADJ
american_scientific_journal-7486	132	19	expressions	expression	NOUN
american_scientific_journal-7486	132	20	x	x	PUNCT
american_scientific_journal-7486	132	21	−	−	PROPN
american_scientific_journal-7486	132	22	n90	n90	NOUN
american_scientific_journal-7486	132	23	−	−	PROPN
american_scientific_journal-7486	132	24	5	5	NUM
american_scientific_journal-7486	132	25	=	=	SYM
american_scientific_journal-7486	132	26	6	6	NUM
american_scientific_journal-7486	132	27	m	m	NOUN
american_scientific_journal-7486	132	28	or	or	CCONJ
american_scientific_journal-7486	132	29	x	x	SYM
american_scientific_journal-7486	132	30	−	−	PROPN
american_scientific_journal-7486	132	31	n90	n90	PROPN
american_scientific_journal-7486	132	32	−	−	PROPN
american_scientific_journal-7486	132	33	7	7	NUM
american_scientific_journal-7486	132	34	=	=	SYM
american_scientific_journal-7486	132	35	6	6	NUM
american_scientific_journal-7486	132	36	m	m	NOUN
american_scientific_journal-7486	132	37	where	where	SCONJ
american_scientific_journal-7486	132	38	n90	n90	PROPN
american_scientific_journal-7486	132	39	is	be	AUX
american_scientific_journal-7486	132	40	the	the	DET
american_scientific_journal-7486	132	41	nearest	near	ADJ
american_scientific_journal-7486	132	42	multiple	multiple	NOUN
american_scientific_journal-7486	132	43	of	of	ADP
american_scientific_journal-7486	132	44	90	90	NUM
american_scientific_journal-7486	132	45	and	and	CCONJ
american_scientific_journal-7486	132	46	m	m	PROPN
american_scientific_journal-7486	132	47	is	be	AUX
american_scientific_journal-7486	132	48	a	a	DET
american_scientific_journal-7486	132	49	whole	whole	ADJ
american_scientific_journal-7486	132	50	number	number	NOUN
american_scientific_journal-7486	132	51	.	.	PUNCT
american_scientific_journal-7486	132	52	”	"	PUNCT
american_scientific_journal-7486	133	1	4.2	4.2	NUM
american_scientific_journal-7486	133	2	.	.	PUNCT
american_scientific_journal-7486	133	3	theorem	theorem	VERB
american_scientific_journal-7486	133	4	american	american	ADJ
american_scientific_journal-7486	133	5	academic	academic	PROPN
american_scientific_journal-7486	133	6	scientific	scientific	ADJ
american_scientific_journal-7486	133	7	research	research	NOUN
american_scientific_journal-7486	133	8	journal	journal	NOUN
american_scientific_journal-7486	133	9	for	for	ADP
american_scientific_journal-7486	133	10	engineering	engineering	NOUN
american_scientific_journal-7486	133	11	,	,	PUNCT
american_scientific_journal-7486	133	12	technology	technology	NOUN
american_scientific_journal-7486	133	13	,	,	PUNCT
american_scientific_journal-7486	133	14	and	and	CCONJ
american_scientific_journal-7486	133	15	sciences	science	NOUN
american_scientific_journal-7486	133	16	(	(	PUNCT
american_scientific_journal-7486	133	17	asrjets	asrjet	NOUN
american_scientific_journal-7486	133	18	)	)	PUNCT
american_scientific_journal-7486	133	19	(	(	PUNCT
american_scientific_journal-7486	133	20	2022	2022	NUM
american_scientific_journal-7486	133	21	)	)	PUNCT
american_scientific_journal-7486	133	22	volume	volume	NOUN
american_scientific_journal-7486	133	23	88	88	NUM
american_scientific_journal-7486	133	24	,	,	PUNCT
american_scientific_journal-7486	133	25	no	no	DET
american_scientific_journal-7486	133	26	1	1	NUM
american_scientific_journal-7486	133	27	,	,	PUNCT
american_scientific_journal-7486	133	28	pp	pp	ADV
american_scientific_journal-7486	133	29	77	77	NUM
american_scientific_journal-7486	133	30	-	-	SYM
american_scientific_journal-7486	133	31	90	90	NUM
american_scientific_journal-7486	133	32	85	85	NUM
american_scientific_journal-7486	133	33	“	"	PUNCT
american_scientific_journal-7486	133	34	let	let	VERB
american_scientific_journal-7486	133	35	x	x	PRON
american_scientific_journal-7486	133	36	be	be	AUX
american_scientific_journal-7486	133	37	an	an	DET
american_scientific_journal-7486	133	38	even	even	ADJ
american_scientific_journal-7486	133	39	number	number	NOUN
american_scientific_journal-7486	133	40	and	and	CCONJ
american_scientific_journal-7486	133	41	x	x	NOUN
american_scientific_journal-7486	133	42	is	be	AUX
american_scientific_journal-7486	133	43	not	not	PART
american_scientific_journal-7486	133	44	a	a	DET
american_scientific_journal-7486	133	45	multiple	multiple	NOUN
american_scientific_journal-7486	133	46	of	of	ADP
american_scientific_journal-7486	133	47	6	6	NUM
american_scientific_journal-7486	133	48	,	,	PUNCT
american_scientific_journal-7486	133	49	then	then	ADV
american_scientific_journal-7486	133	50	every	every	DET
american_scientific_journal-7486	133	51	prime	prime	ADJ
american_scientific_journal-7486	133	52	number	number	NOUN
american_scientific_journal-7486	133	53	except	except	SCONJ
american_scientific_journal-7486	133	54	3	3	NUM
american_scientific_journal-7486	133	55	is	be	AUX
american_scientific_journal-7486	133	56	a	a	DET
american_scientific_journal-7486	133	57	collatz	collatz	NOUN
american_scientific_journal-7486	133	58	number	number	NOUN
american_scientific_journal-7486	133	59	of	of	ADP
american_scientific_journal-7486	133	60	some	some	DET
american_scientific_journal-7486	133	61	x.	x.	NOUN
american_scientific_journal-7486	133	62	”	"	PUNCT
american_scientific_journal-7486	133	63	4.4	4.4	NUM
american_scientific_journal-7486	133	64	.	.	PUNCT
american_scientific_journal-7486	134	1	corollary	corollary	ADJ
american_scientific_journal-7486	134	2	“	"	PUNCT
american_scientific_journal-7486	134	3	every	every	DET
american_scientific_journal-7486	134	4	prime	prime	ADJ
american_scientific_journal-7486	134	5	number	number	NOUN
american_scientific_journal-7486	134	6	greater	great	ADJ
american_scientific_journal-7486	134	7	than	than	ADP
american_scientific_journal-7486	134	8	30	30	NUM
american_scientific_journal-7486	134	9	can	can	AUX
american_scientific_journal-7486	134	10	be	be	AUX
american_scientific_journal-7486	134	11	obtained	obtain	VERB
american_scientific_journal-7486	134	12	from	from	ADP
american_scientific_journal-7486	134	13	the	the	DET
american_scientific_journal-7486	134	14	sequence	sequence	NOUN
american_scientific_journal-7486	134	15	of	of	ADP
american_scientific_journal-7486	134	16	numbers	number	NOUN
american_scientific_journal-7486	134	17	:	:	PUNCT
american_scientific_journal-7486	134	18	n30	n30	PROPN
american_scientific_journal-7486	134	19	+	+	CCONJ
american_scientific_journal-7486	134	20	1	1	NUM
american_scientific_journal-7486	134	21	+	+	NUM
american_scientific_journal-7486	134	22	6	6	NUM
american_scientific_journal-7486	134	23	+	+	NUM
american_scientific_journal-7486	134	24	4	4	NUM
american_scientific_journal-7486	134	25	+	+	SYM
american_scientific_journal-7486	134	26	2	2	NUM
american_scientific_journal-7486	134	27	+	+	CCONJ
american_scientific_journal-7486	134	28	4	4	NUM
american_scientific_journal-7486	134	29	+	+	SYM
american_scientific_journal-7486	134	30	2	2	NUM
american_scientific_journal-7486	134	31	+	+	CCONJ
american_scientific_journal-7486	134	32	4	4	NUM
american_scientific_journal-7486	134	33	+	+	SYM
american_scientific_journal-7486	134	34	6	6	NUM
american_scientific_journal-7486	134	35	,	,	PUNCT
american_scientific_journal-7486	134	36	where	where	SCONJ
american_scientific_journal-7486	134	37	n30	n30	PROPN
american_scientific_journal-7486	134	38	is	be	AUX
american_scientific_journal-7486	134	39	the	the	DET
american_scientific_journal-7486	134	40	nearest	near	ADJ
american_scientific_journal-7486	134	41	multiple	multiple	NOUN
american_scientific_journal-7486	134	42	of	of	ADP
american_scientific_journal-7486	134	43	30	30	NUM
american_scientific_journal-7486	134	44	less	less	ADJ
american_scientific_journal-7486	134	45	than	than	ADP
american_scientific_journal-7486	134	46	the	the	DET
american_scientific_journal-7486	134	47	given	give	VERB
american_scientific_journal-7486	134	48	prime	prime	NOUN
american_scientific_journal-7486	134	49	and	and	CCONJ
american_scientific_journal-7486	134	50	is	be	AUX
american_scientific_journal-7486	134	51	a	a	DET
american_scientific_journal-7486	134	52	whole	whole	ADJ
american_scientific_journal-7486	134	53	number	number	NOUN
american_scientific_journal-7486	134	54	.	.	PUNCT
american_scientific_journal-7486	134	55	”	"	PUNCT
american_scientific_journal-7486	135	1	6	6	NUM
american_scientific_journal-7486	135	2	.	.	PUNCT
american_scientific_journal-7486	135	3	conflict	conflict	NOUN
american_scientific_journal-7486	135	4	of	of	ADP
american_scientific_journal-7486	135	5	interest	interest	NOUN
american_scientific_journal-7486	135	6	statement	statement	NOUN
american_scientific_journal-7486	135	7	the	the	DET
american_scientific_journal-7486	135	8	author	author	NOUN
american_scientific_journal-7486	135	9	declares	declare	VERB
american_scientific_journal-7486	135	10	that	that	SCONJ
american_scientific_journal-7486	135	11	there	there	PRON
american_scientific_journal-7486	135	12	is	be	VERB
american_scientific_journal-7486	135	13	no	no	DET
american_scientific_journal-7486	135	14	conflict	conflict	NOUN
american_scientific_journal-7486	135	15	of	of	ADP
american_scientific_journal-7486	135	16	interest	interest	NOUN
american_scientific_journal-7486	135	17	in	in	ADP
american_scientific_journal-7486	135	18	this	this	DET
american_scientific_journal-7486	135	19	paper	paper	NOUN
american_scientific_journal-7486	135	20	.	.	PUNCT
american_scientific_journal-7486	136	1	the	the	DET
american_scientific_journal-7486	136	2	author	author	NOUN
american_scientific_journal-7486	136	3	declare	declare	VERB
american_scientific_journal-7486	136	4	that	that	SCONJ
american_scientific_journal-7486	136	5	there	there	PRON
american_scientific_journal-7486	136	6	are	be	VERB
american_scientific_journal-7486	136	7	no	no	DET
american_scientific_journal-7486	136	8	other	other	ADJ
american_scientific_journal-7486	136	9	financial	financial	ADJ
american_scientific_journal-7486	136	10	relationships	relationship	NOUN
american_scientific_journal-7486	136	11	with	with	ADP
american_scientific_journal-7486	136	12	any	any	DET
american_scientific_journal-7486	136	13	organizations	organization	NOUN
american_scientific_journal-7486	136	14	that	that	PRON
american_scientific_journal-7486	136	15	might	might	AUX
american_scientific_journal-7486	136	16	have	have	VERB
american_scientific_journal-7486	136	17	an	an	DET
american_scientific_journal-7486	136	18	interest	interest	NOUN
american_scientific_journal-7486	136	19	in	in	ADP
american_scientific_journal-7486	136	20	the	the	DET
american_scientific_journal-7486	136	21	submitted	submit	VERB
american_scientific_journal-7486	136	22	work	work	NOUN
american_scientific_journal-7486	136	23	.	.	PUNCT
american_scientific_journal-7486	137	1	references	reference	NOUN
american_scientific_journal-7486	137	2	[	[	X
american_scientific_journal-7486	137	3	1	1	NUM
american_scientific_journal-7486	137	4	]	]	PUNCT
american_scientific_journal-7486	137	5	m.	m.	PROPN
american_scientific_journal-7486	137	6	dorsey	dorsey	PROPN
american_scientific_journal-7486	137	7	and	and	CCONJ
american_scientific_journal-7486	137	8	s.	s.	PROPN
american_scientific_journal-7486	137	9	zachary	zachary	PROPN
american_scientific_journal-7486	137	10	.	.	PUNCT
american_scientific_journal-7486	138	1	“	"	PUNCT
american_scientific_journal-7486	138	2	methods	method	NOUN
american_scientific_journal-7486	138	3	of	of	ADP
american_scientific_journal-7486	138	4	primality	primality	NOUN
american_scientific_journal-7486	138	5	testing	testing	NOUN
american_scientific_journal-7486	138	6	.	.	PUNCT
american_scientific_journal-7486	138	7	”	"	PUNCT
american_scientific_journal-7486	139	1	smit	smit	PROPN
american_scientific_journal-7486	139	2	undergraduate	undergraduate	PROPN
american_scientific_journal-7486	139	3	journal	journal	PROPN
american_scientific_journal-7486	139	4	of	of	ADP
american_scientific_journal-7486	139	5	mathematics	mathematic	NOUN
american_scientific_journal-7486	139	6	,	,	PUNCT
american_scientific_journal-7486	139	7	vol	vol	NOUN
american_scientific_journal-7486	139	8	(	(	PUNCT
american_scientific_journal-7486	139	9	1	1	NUM
american_scientific_journal-7486	139	10	)	)	PUNCT
american_scientific_journal-7486	139	11	,	,	PUNCT
american_scientific_journal-7486	139	12	133	133	NUM
american_scientific_journal-7486	139	13	-	-	SYM
american_scientific_journal-7486	139	14	141	141	NUM
american_scientific_journal-7486	139	15	,	,	PUNCT
american_scientific_journal-7486	139	16	1999	1999	NUM
american_scientific_journal-7486	139	17	.	.	PUNCT
american_scientific_journal-7486	140	1	[	[	X
american_scientific_journal-7486	140	2	2	2	NUM
american_scientific_journal-7486	140	3	]	]	PUNCT
american_scientific_journal-7486	140	4	s.	s.	PROPN
american_scientific_journal-7486	140	5	ishmukhametov	ishmukhametov	PROPN
american_scientific_journal-7486	140	6	and	and	CCONJ
american_scientific_journal-7486	140	7	b.	b.	PROPN
american_scientific_journal-7486	140	8	mubarakov	mubarakov	PROPN
american_scientific_journal-7486	140	9	.	.	PUNCT
american_scientific_journal-7486	141	1	“	"	PUNCT
american_scientific_journal-7486	141	2	on	on	ADP
american_scientific_journal-7486	141	3	practical	practical	ADJ
american_scientific_journal-7486	141	4	aspects	aspect	NOUN
american_scientific_journal-7486	141	5	of	of	ADP
american_scientific_journal-7486	141	6	the	the	DET
american_scientific_journal-7486	141	7	miller	miller	PROPN
american_scientific_journal-7486	141	8	-	-	PUNCT
american_scientific_journal-7486	141	9	rabin	rabin	PROPN
american_scientific_journal-7486	141	10	primality	primality	PROPN
american_scientific_journal-7486	141	11	test	test	NOUN
american_scientific_journal-7486	141	12	.	.	PUNCT
american_scientific_journal-7486	141	13	”	"	PUNCT
american_scientific_journal-7486	141	14	lobachevskii	lobachevskii	PROPN
american_scientific_journal-7486	141	15	journal	journal	NOUN
american_scientific_journal-7486	141	16	of	of	ADP
american_scientific_journal-7486	141	17	mathematics	mathematics	PROPN
american_scientific_journal-7486	141	18	,	,	PUNCT
american_scientific_journal-7486	141	19	vol	vol	NOUN
american_scientific_journal-7486	141	20	.	.	PUNCT
american_scientific_journal-7486	141	21	(	(	PUNCT
american_scientific_journal-7486	141	22	34)4	34)4	NUM
american_scientific_journal-7486	141	23	,	,	PUNCT
american_scientific_journal-7486	141	24	pp.304	pp.304	PROPN
american_scientific_journal-7486	141	25	-	-	PUNCT
american_scientific_journal-7486	141	26	312	312	NUM
american_scientific_journal-7486	141	27	,	,	PUNCT
american_scientific_journal-7486	141	28	2013	2013	NUM
american_scientific_journal-7486	141	29	.	.	PUNCT
american_scientific_journal-7486	142	1	[	[	X
american_scientific_journal-7486	142	2	3	3	X
american_scientific_journal-7486	142	3	]	]	X
american_scientific_journal-7486	142	4	rosenberg	rosenberg	PROPN
american_scientific_journal-7486	142	5	and	and	CCONJ
american_scientific_journal-7486	142	6	burt	burt	PROPN
american_scientific_journal-7486	142	7	.	.	PUNCT
american_scientific_journal-7486	143	1	“	"	PUNCT
american_scientific_journal-7486	143	2	the	the	DET
american_scientific_journal-7486	143	3	solovay	solovay	NOUN
american_scientific_journal-7486	143	4	-	-	PUNCT
american_scientific_journal-7486	143	5	strassen	strassen	NOUN
american_scientific_journal-7486	143	6	primality	primality	PROPN
american_scientific_journal-7486	143	7	test	test	NOUN
american_scientific_journal-7486	143	8	.	.	PUNCT
american_scientific_journal-7486	143	9	”	"	PUNCT
american_scientific_journal-7486	144	1	university	university	PROPN
american_scientific_journal-7486	144	2	of	of	ADP
american_scientific_journal-7486	144	3	miami	miami	PROPN
american_scientific_journal-7486	144	4	.	.	PUNCT
american_scientific_journal-7486	145	1	department	department	PROPN
american_scientific_journal-7486	145	2	of	of	ADP
american_scientific_journal-7486	145	3	computer	computer	NOUN
american_scientific_journal-7486	145	4	science	science	NOUN
american_scientific_journal-7486	145	5	.	.	PUNCT
american_scientific_journal-7486	146	1	miami	miami	PROPN
american_scientific_journal-7486	146	2	,	,	PUNCT
american_scientific_journal-7486	146	3	1993	1993	NUM
american_scientific_journal-7486	146	4	.	.	PUNCT
american_scientific_journal-7486	147	1	[	[	X
american_scientific_journal-7486	147	2	4	4	NUM
american_scientific_journal-7486	147	3	]	]	PUNCT
american_scientific_journal-7486	147	4	m.	m.	NOUN
american_scientific_journal-7486	147	5	agrawal	agrawal	PROPN
american_scientific_journal-7486	147	6	;	;	PUNCT
american_scientific_journal-7486	147	7	n.	n.	PROPN
american_scientific_journal-7486	147	8	kayal	kayal	PROPN
american_scientific_journal-7486	147	9	;	;	PUNCT
american_scientific_journal-7486	147	10	n	n	PRON
american_scientific_journal-7486	147	11	saxena	saxena	PROPN
american_scientific_journal-7486	147	12	.	.	PUNCT
american_scientific_journal-7486	148	1	"	"	PUNCT
american_scientific_journal-7486	148	2	primes	prime	NOUN
american_scientific_journal-7486	148	3	is	be	AUX
american_scientific_journal-7486	148	4	in	in	ADP
american_scientific_journal-7486	148	5	p	p	X
american_scientific_journal-7486	148	6	"	"	PUNCT
american_scientific_journal-7486	148	7	(	(	PUNCT
american_scientific_journal-7486	148	8	pdf	pdf	NOUN
american_scientific_journal-7486	148	9	)	)	PUNCT
american_scientific_journal-7486	148	10	.	.	PUNCT
american_scientific_journal-7486	149	1	annals	annal	NOUN
american_scientific_journal-7486	149	2	of	of	ADP
american_scientific_journal-7486	149	3	mathematics	mathematic	NOUN
american_scientific_journal-7486	149	4	.	.	PUNCT
american_scientific_journal-7486	150	1	vol	vol	NOUN
american_scientific_journal-7486	150	2	.	.	PUNCT
american_scientific_journal-7486	151	1	160	160	NUM
american_scientific_journal-7486	151	2	(	(	PUNCT
american_scientific_journal-7486	151	3	2	2	NUM
american_scientific_journal-7486	151	4	)	)	PUNCT
american_scientific_journal-7486	151	5	,	,	PUNCT
american_scientific_journal-7486	151	6	pp	pp	ADP
american_scientific_journal-7486	151	7	.	.	PUNCT
american_scientific_journal-7486	152	1	781–793	781–793	NUM
american_scientific_journal-7486	152	2	,	,	PUNCT
american_scientific_journal-7486	152	3	2004	2004	NUM
american_scientific_journal-7486	152	4	.	.	PUNCT
american_scientific_journal-7486	153	1	[	[	X
american_scientific_journal-7486	153	2	5	5	NUM
american_scientific_journal-7486	153	3	]	]	X
american_scientific_journal-7486	153	4	cohen	cohen	PROPN
american_scientific_journal-7486	153	5	,	,	PUNCT
american_scientific_journal-7486	153	6	henri	henri	PROPN
american_scientific_journal-7486	153	7	;	;	PUNCT
american_scientific_journal-7486	153	8	lenstra	lenstra	PROPN
american_scientific_journal-7486	153	9	,	,	PUNCT
american_scientific_journal-7486	153	10	w	w	PROPN
american_scientific_journal-7486	153	11	,	,	PUNCT
american_scientific_journal-7486	153	12	hendrik	hendrik	PROPN
american_scientific_journal-7486	153	13	.	.	PUNCT
american_scientific_journal-7486	153	14	,	,	PUNCT
american_scientific_journal-7486	153	15	jr	jr	PROPN
american_scientific_journal-7486	153	16	.	.	PUNCT
american_scientific_journal-7486	153	17	"	"	PUNCT
american_scientific_journal-7486	153	18	primality	primality	NOUN
american_scientific_journal-7486	153	19	testing	testing	NOUN
american_scientific_journal-7486	153	20	and	and	CCONJ
american_scientific_journal-7486	153	21	jacobi	jacobi	PROPN
american_scientific_journal-7486	153	22	sums	sums	PROPN
american_scientific_journal-7486	153	23	"	"	PUNCT
american_scientific_journal-7486	153	24	.	.	PUNCT
american_scientific_journal-7486	154	1	mathematics	mathematic	NOUN
american_scientific_journal-7486	154	2	of	of	ADP
american_scientific_journal-7486	154	3	computation	computation	NOUN
american_scientific_journal-7486	154	4	.	.	PUNCT
american_scientific_journal-7486	155	1	vol	vol	NOUN
american_scientific_journal-7486	155	2	.	.	PROPN
american_scientific_journal-7486	156	1	42	42	NUM
american_scientific_journal-7486	156	2	,	,	PUNCT
american_scientific_journal-7486	156	3	(	(	PUNCT
american_scientific_journal-7486	156	4	165	165	NUM
american_scientific_journal-7486	156	5	)	)	PUNCT
american_scientific_journal-7486	156	6	,	,	PUNCT
american_scientific_journal-7486	156	7	pp	pp	ADP
american_scientific_journal-7486	156	8	.	.	PUNCT
american_scientific_journal-7486	157	1	297–330	297–330	NUM
american_scientific_journal-7486	157	2	,	,	PUNCT
american_scientific_journal-7486	157	3	1984	1984	NUM
american_scientific_journal-7486	157	4	.	.	PUNCT
american_scientific_journal-7486	158	1	[	[	X
american_scientific_journal-7486	158	2	6	6	NUM
american_scientific_journal-7486	158	3	]	]	X
american_scientific_journal-7486	158	4	l.k	l.k	PROPN
american_scientific_journal-7486	158	5	.	.	PROPN
american_scientific_journal-7486	158	6	hua	hua	PROPN
american_scientific_journal-7486	158	7	.	.	PUNCT
american_scientific_journal-7486	159	1	“	"	PUNCT
american_scientific_journal-7486	159	2	introduction	introduction	NOUN
american_scientific_journal-7486	159	3	to	to	ADP
american_scientific_journal-7486	159	4	number	number	NOUN
american_scientific_journal-7486	159	5	theory	theory	NOUN
american_scientific_journal-7486	159	6	”	"	PUNCT
american_scientific_journal-7486	159	7	.	.	PUNCT
american_scientific_journal-7486	160	1	springer	springer	PROPN
american_scientific_journal-7486	160	2	science	science	PROPN
american_scientific_journal-7486	160	3	&	&	CCONJ
american_scientific_journal-7486	160	4	business	business	NOUN
american_scientific_journal-7486	160	5	media	medium	NOUN
american_scientific_journal-7486	160	6	,	,	PUNCT
american_scientific_journal-7486	160	7	2012	2012	NUM
american_scientific_journal-7486	160	8	.	.	PUNCT
american_scientific_journal-7486	161	1	[	[	X
american_scientific_journal-7486	161	2	7	7	X
american_scientific_journal-7486	161	3	]	]	X
american_scientific_journal-7486	161	4	i.n	i.n	PROPN
american_scientific_journal-7486	161	5	.	.	PROPN
american_scientific_journal-7486	161	6	herstein	herstein	PROPN
american_scientific_journal-7486	161	7	.	.	PUNCT
american_scientific_journal-7486	162	1	“	"	PUNCT
american_scientific_journal-7486	162	2	topics	topic	NOUN
american_scientific_journal-7486	162	3	in	in	ADP
american_scientific_journal-7486	162	4	algebra	algebra	NOUN
american_scientific_journal-7486	162	5	”	"	PUNCT
american_scientific_journal-7486	162	6	.	.	PUNCT
american_scientific_journal-7486	163	1	john	john	PROPN
american_scientific_journal-7486	163	2	wiley	wiley	PROPN
american_scientific_journal-7486	163	3	&	&	CCONJ
american_scientific_journal-7486	163	4	sons	son	NOUN
american_scientific_journal-7486	163	5	,	,	PUNCT
american_scientific_journal-7486	163	6	2006	2006	NUM
american_scientific_journal-7486	163	7	.	.	PUNCT
american_scientific_journal-7486	164	1	[	[	X
american_scientific_journal-7486	164	2	8	8	NUM
american_scientific_journal-7486	164	3	]	]	PUNCT
american_scientific_journal-7486	164	4	p.	p.	NOUN
american_scientific_journal-7486	164	5	honner	honner	PROPN
american_scientific_journal-7486	164	6	.	.	PUNCT
american_scientific_journal-7486	165	1	“	"	PUNCT
american_scientific_journal-7486	165	2	the	the	DET
american_scientific_journal-7486	165	3	simple	simple	ADJ
american_scientific_journal-7486	165	4	math	math	NOUN
american_scientific_journal-7486	165	5	problem	problem	NOUN
american_scientific_journal-7486	165	6	we	we	PRON
american_scientific_journal-7486	165	7	still	still	ADV
american_scientific_journal-7486	165	8	ca	can	AUX
american_scientific_journal-7486	165	9	n’t	not	PART
american_scientific_journal-7486	165	10	solve	solve	VERB
american_scientific_journal-7486	165	11	”	"	PUNCT
american_scientific_journal-7486	165	12	.	.	PUNCT
american_scientific_journal-7486	166	1	internet	internet	NOUN
american_scientific_journal-7486	166	2	:	:	PUNCT
american_scientific_journal-7486	166	3	www.quantamagazine.org.html	www.quantamagazine.org.html	PROPN
american_scientific_journal-7486	166	4	,	,	PUNCT
american_scientific_journal-7486	166	5	sep	sep	PROPN
american_scientific_journal-7486	166	6	.	.	PROPN
american_scientific_journal-7486	166	7	20	20	NUM
american_scientific_journal-7486	166	8	,	,	PUNCT
american_scientific_journal-7486	166	9	2020	2020	NUM
american_scientific_journal-7486	167	1	[	[	X
american_scientific_journal-7486	167	2	oct.10	oct.10	NOUN
american_scientific_journal-7486	167	3	,	,	PUNCT
american_scientific_journal-7486	167	4	2020	2020	NUM
american_scientific_journal-7486	167	5	]	]	PUNCT
american_scientific_journal-7486	168	1	[	[	X
american_scientific_journal-7486	168	2	9	9	NUM
american_scientific_journal-7486	168	3	]	]	PUNCT
american_scientific_journal-7486	168	4	k.	k.	PROPN
american_scientific_journal-7486	168	5	hartnet	hartnet	PROPN
american_scientific_journal-7486	168	6	.	.	PUNCT
american_scientific_journal-7486	169	1	“	"	PUNCT
american_scientific_journal-7486	169	2	mathematician	mathematician	NOUN
american_scientific_journal-7486	169	3	proves	prove	VERB
american_scientific_journal-7486	169	4	huge	huge	ADJ
american_scientific_journal-7486	169	5	result	result	NOUN
american_scientific_journal-7486	169	6	on	on	ADP
american_scientific_journal-7486	169	7	‘	'	PUNCT
american_scientific_journal-7486	169	8	dangerous	dangerous	ADJ
american_scientific_journal-7486	169	9	’	'	PUNCT
american_scientific_journal-7486	169	10	problem	problem	NOUN
american_scientific_journal-7486	169	11	.	.	PUNCT
american_scientific_journal-7486	169	12	”	"	PUNCT
american_scientific_journal-7486	169	13	internet	internet	NOUN
american_scientific_journal-7486	169	14	:	:	PUNCT
american_scientific_journal-7486	169	15	www.quantamagazine.org.html	www.quantamagazine.org.html	PROPN
american_scientific_journal-7486	169	16	,	,	PUNCT
american_scientific_journal-7486	169	17	dec	dec	PROPN
american_scientific_journal-7486	169	18	.	.	PROPN
american_scientific_journal-7486	169	19	11	11	NUM
american_scientific_journal-7486	169	20	,	,	PUNCT
american_scientific_journal-7486	169	21	2019	2019	NUM
american_scientific_journal-7486	169	22	[	[	X
american_scientific_journal-7486	169	23	may.30	may.30	NOUN
american_scientific_journal-7486	169	24	,	,	PUNCT
american_scientific_journal-7486	169	25	2020	2020	NUM
american_scientific_journal-7486	169	26	]	]	PUNCT
american_scientific_journal-7486	169	27	http://www.cse.iitk.ac.in/users/manindra/algebra/primality_v6.pdf	http://www.cse.iitk.ac.in/users/manindra/algebra/primality_v6.pdf	PROPN
american_scientific_journal-7486	169	28	https://en.wikipedia.org/wiki/annals_of_mathematics	https://en.wikipedia.org/wiki/annals_of_mathematic	NOUN
american_scientific_journal-7486	169	29	https://en.wikipedia.org/wiki/henri_cohen_(number_theorist	https://en.wikipedia.org/wiki/henri_cohen_(number_theorist	NOUN
american_scientific_journal-7486	169	30	)	)	PUNCT
american_scientific_journal-7486	169	31	https://en.wikipedia.org/wiki/hendrik_lenstra	https://en.wikipedia.org/wiki/hendrik_lenstra	PROPN
american_scientific_journal-7486	169	32	https://doi.org/10.2307%2f2007581	https://doi.org/10.2307%2f2007581	PROPN
american_scientific_journal-7486	169	33	https://en.wikipedia.org/wiki/mathematics_of_computation	https://en.wikipedia.org/wiki/mathematics_of_computation	PROPN
american_scientific_journal-7486	169	34	https://en.wikipedia.org/wiki/mathematics_of_computation	https://en.wikipedia.org/wiki/mathematics_of_computation	PROPN
american_scientific_journal-7486	169	35	http://www.quantamagazine.org.html/	http://www.quantamagazine.org.html/	PROPN
american_scientific_journal-7486	169	36	http://www.quantamagazine.org.html/	http://www.quantamagazine.org.html/	PROPN
american_scientific_journal-7486	169	37	american	american	ADJ
american_scientific_journal-7486	169	38	academic	academic	ADJ
american_scientific_journal-7486	169	39	scientific	scientific	ADJ
american_scientific_journal-7486	169	40	research	research	NOUN
american_scientific_journal-7486	169	41	journal	journal	NOUN
american_scientific_journal-7486	169	42	for	for	ADP
american_scientific_journal-7486	169	43	engineering	engineering	NOUN
american_scientific_journal-7486	169	44	,	,	PUNCT
american_scientific_journal-7486	169	45	technology	technology	NOUN
american_scientific_journal-7486	169	46	,	,	PUNCT
american_scientific_journal-7486	169	47	and	and	CCONJ
american_scientific_journal-7486	169	48	sciences	science	NOUN
american_scientific_journal-7486	169	49	(	(	PUNCT
american_scientific_journal-7486	169	50	asrjets	asrjet	NOUN
american_scientific_journal-7486	169	51	)	)	PUNCT
american_scientific_journal-7486	169	52	(	(	PUNCT
american_scientific_journal-7486	169	53	2022	2022	NUM
american_scientific_journal-7486	169	54	)	)	PUNCT
american_scientific_journal-7486	169	55	volume	volume	NOUN
american_scientific_journal-7486	169	56	88	88	NUM
american_scientific_journal-7486	169	57	,	,	PUNCT
american_scientific_journal-7486	169	58	no	no	DET
american_scientific_journal-7486	169	59	1	1	NUM
american_scientific_journal-7486	169	60	,	,	PUNCT
american_scientific_journal-7486	169	61	pp	pp	ADV
american_scientific_journal-7486	169	62	77	77	NUM
american_scientific_journal-7486	169	63	-	-	SYM
american_scientific_journal-7486	169	64	90	90	NUM
american_scientific_journal-7486	169	65	86	86	NUM
american_scientific_journal-7486	169	66	appendix	appendix	NOUN
american_scientific_journal-7486	169	67	1	1	NUM
american_scientific_journal-7486	169	68	matlab	matlab	PROPN
american_scientific_journal-7486	169	69	code	code	NOUN
american_scientific_journal-7486	169	70	for	for	ADP
american_scientific_journal-7486	169	71	primality	primality	NOUN
american_scientific_journal-7486	169	72	test	test	NOUN
american_scientific_journal-7486	169	73	theorem	theorem	VERB
american_scientific_journal-7486	169	74	2.1	2.1	NUM
american_scientific_journal-7486	169	75	.	.	PUNCT
american_scientific_journal-7486	170	1	clc	clc	PROPN
american_scientific_journal-7486	170	2	clear	clear	ADJ
american_scientific_journal-7486	170	3	all	all	DET
american_scientific_journal-7486	170	4	flag	flag	NOUN
american_scientific_journal-7486	170	5	=	=	NOUN
american_scientific_journal-7486	170	6	0	0	NUM
american_scientific_journal-7486	170	7	;	;	PUNCT
american_scientific_journal-7486	170	8	input_no	input_no	NOUN
american_scientific_journal-7486	170	9	=	=	SYM
american_scientific_journal-7486	170	10	input	input	NOUN
american_scientific_journal-7486	170	11	(	(	PUNCT
american_scientific_journal-7486	170	12	'	'	PUNCT
american_scientific_journal-7486	170	13	enter	enter	VERB
american_scientific_journal-7486	170	14	the	the	DET
american_scientific_journal-7486	170	15	number	number	NOUN
american_scientific_journal-7486	170	16	'	'	PUNCT
american_scientific_journal-7486	170	17	)	)	PUNCT
american_scientific_journal-7486	170	18	;	;	PUNCT
american_scientific_journal-7486	170	19	if	if	SCONJ
american_scientific_journal-7486	170	20	(	(	PUNCT
american_scientific_journal-7486	170	21	input_no<=1	input_no<=1	PROPN
american_scientific_journal-7486	170	22	)	)	PUNCT
american_scientific_journal-7486	170	23	fprintf	fprintf	NOUN
american_scientific_journal-7486	170	24	(	(	PUNCT
american_scientific_journal-7486	170	25	'	'	PUNCT
american_scientific_journal-7486	170	26	please	please	INTJ
american_scientific_journal-7486	170	27	enter	enter	VERB
american_scientific_journal-7486	170	28	a	a	DET
american_scientific_journal-7486	170	29	valid	valid	ADJ
american_scientific_journal-7486	170	30	number	number	NOUN
american_scientific_journal-7486	170	31	'	'	PUNCT
american_scientific_journal-7486	170	32	)	)	PUNCT
american_scientific_journal-7486	170	33	;	;	PUNCT
american_scientific_journal-7486	170	34	elseif	elseif	NOUN
american_scientific_journal-7486	170	35	(	(	PUNCT
american_scientific_journal-7486	170	36	input_no==2||input_no==3	input_no==2||input_no==3	PROPN
american_scientific_journal-7486	170	37	)	)	PUNCT
american_scientific_journal-7486	170	38	fprintf	fprintf	NOUN
american_scientific_journal-7486	170	39	(	(	PUNCT
american_scientific_journal-7486	170	40	'	'	PUNCT
american_scientific_journal-7486	170	41	the	the	DET
american_scientific_journal-7486	170	42	entered	enter	VERB
american_scientific_journal-7486	170	43	number	number	NOUN
american_scientific_journal-7486	170	44	is	be	AUX
american_scientific_journal-7486	170	45	a	a	DET
american_scientific_journal-7486	170	46	prime	prime	ADJ
american_scientific_journal-7486	170	47	number	number	NOUN
american_scientific_journal-7486	170	48	'	'	PUNCT
american_scientific_journal-7486	170	49	)	)	PUNCT
american_scientific_journal-7486	170	50	;	;	PUNCT
american_scientific_journal-7486	170	51	else	else	ADV
american_scientific_journal-7486	170	52	flag=0	flag=0	NUM
american_scientific_journal-7486	170	53	;	;	PUNCT
american_scientific_journal-7486	170	54	ninety_n1	ninety_n1	NOUN
american_scientific_journal-7486	170	55	=	=	PUNCT
american_scientific_journal-7486	170	56	floor	floor	NOUN
american_scientific_journal-7486	170	57	(	(	PUNCT
american_scientific_journal-7486	170	58	input_no/90	input_no/90	PROPN
american_scientific_journal-7486	170	59	)	)	PUNCT
american_scientific_journal-7486	170	60	;	;	PUNCT
american_scientific_journal-7486	171	1	n1	n1	NOUN
american_scientific_journal-7486	171	2	=	=	SYM
american_scientific_journal-7486	171	3	input_no	input_no	X
american_scientific_journal-7486	171	4	(	(	PUNCT
american_scientific_journal-7486	171	5	ninety_n1	ninety_n1	NOUN
american_scientific_journal-7486	171	6	*	*	SYM
american_scientific_journal-7486	171	7	90	90	NUM
american_scientific_journal-7486	171	8	)	)	PUNCT
american_scientific_journal-7486	171	9	5	5	NUM
american_scientific_journal-7486	171	10	;	;	PUNCT
american_scientific_journal-7486	171	11	no1	no1	X
american_scientific_journal-7486	171	12	=	=	NOUN
american_scientific_journal-7486	171	13	n1	n1	NOUN
american_scientific_journal-7486	171	14	/	/	SYM
american_scientific_journal-7486	171	15	6	6	NUM
american_scientific_journal-7486	171	16	;	;	PUNCT
american_scientific_journal-7486	171	17	ninety_n2	ninety_n2	NOUN
american_scientific_journal-7486	171	18	=	=	NOUN
american_scientific_journal-7486	171	19	floor	floor	NOUN
american_scientific_journal-7486	171	20	(	(	PUNCT
american_scientific_journal-7486	171	21	input_no/90	input_no/90	PROPN
american_scientific_journal-7486	171	22	)	)	PUNCT
american_scientific_journal-7486	171	23	;	;	PUNCT
american_scientific_journal-7486	171	24	n2	n2	ADJ
american_scientific_journal-7486	171	25	=	=	NOUN
american_scientific_journal-7486	171	26	input_no	input_no	X
american_scientific_journal-7486	171	27	(	(	PUNCT
american_scientific_journal-7486	171	28	ninety_n2	ninety_n2	NOUN
american_scientific_journal-7486	171	29	*	*	SYM
american_scientific_journal-7486	171	30	90	90	NUM
american_scientific_journal-7486	171	31	)	)	PUNCT
american_scientific_journal-7486	171	32	-7	-7	PUNCT
american_scientific_journal-7486	171	33	;	;	PUNCT
american_scientific_journal-7486	171	34	no2	no2	NOUN
american_scientific_journal-7486	171	35	=	=	SYM
american_scientific_journal-7486	171	36	n2	n2	PROPN
american_scientific_journal-7486	171	37	/	/	SYM
american_scientific_journal-7486	171	38	6	6	NUM
american_scientific_journal-7486	171	39	;	;	PUNCT
american_scientific_journal-7486	171	40	if	if	SCONJ
american_scientific_journal-7486	171	41	(	(	PUNCT
american_scientific_journal-7486	171	42	mod	mod	X
american_scientific_journal-7486	171	43	(	(	PUNCT
american_scientific_journal-7486	171	44	no1,1)==0	no1,1)==0	ADJ
american_scientific_journal-7486	171	45	)	)	PUNCT
american_scientific_journal-7486	171	46	flag=1	flag=1	PROPN
american_scientific_journal-7486	171	47	;	;	PUNCT
american_scientific_journal-7486	171	48	elseif	elseif	NOUN
american_scientific_journal-7486	171	49	(	(	PUNCT
american_scientific_journal-7486	171	50	mod	mod	X
american_scientific_journal-7486	171	51	(	(	PUNCT
american_scientific_journal-7486	171	52	no2,1)==0	no2,1)==0	ADJ
american_scientific_journal-7486	171	53	)	)	PUNCT
american_scientific_journal-7486	171	54	flag=1	flag=1	PROPN
american_scientific_journal-7486	171	55	;	;	PUNCT
american_scientific_journal-7486	171	56	american	american	ADJ
american_scientific_journal-7486	171	57	academic	academic	ADJ
american_scientific_journal-7486	171	58	scientific	scientific	ADJ
american_scientific_journal-7486	171	59	research	research	NOUN
american_scientific_journal-7486	171	60	journal	journal	NOUN
american_scientific_journal-7486	171	61	for	for	ADP
american_scientific_journal-7486	171	62	engineering	engineering	NOUN
american_scientific_journal-7486	171	63	,	,	PUNCT
american_scientific_journal-7486	171	64	technology	technology	NOUN
american_scientific_journal-7486	171	65	,	,	PUNCT
american_scientific_journal-7486	171	66	and	and	CCONJ
american_scientific_journal-7486	171	67	sciences	science	NOUN
american_scientific_journal-7486	171	68	(	(	PUNCT
american_scientific_journal-7486	171	69	asrjets	asrjet	NOUN
american_scientific_journal-7486	171	70	)	)	PUNCT
american_scientific_journal-7486	171	71	(	(	PUNCT
american_scientific_journal-7486	171	72	2022	2022	NUM
american_scientific_journal-7486	171	73	)	)	PUNCT
american_scientific_journal-7486	171	74	volume	volume	NOUN
american_scientific_journal-7486	171	75	88	88	NUM
american_scientific_journal-7486	171	76	,	,	PUNCT
american_scientific_journal-7486	171	77	no	no	DET
american_scientific_journal-7486	171	78	1	1	NUM
american_scientific_journal-7486	171	79	,	,	PUNCT
american_scientific_journal-7486	171	80	pp	pp	ADV
american_scientific_journal-7486	171	81	77	77	NUM
american_scientific_journal-7486	171	82	-	-	SYM
american_scientific_journal-7486	171	83	90	90	NUM
american_scientific_journal-7486	171	84	87	87	NUM
american_scientific_journal-7486	171	85	end	end	NOUN
american_scientific_journal-7486	171	86	if	if	SCONJ
american_scientific_journal-7486	171	87	(	(	PUNCT
american_scientific_journal-7486	171	88	flag==1	flag==1	NOUN
american_scientific_journal-7486	171	89	)	)	PUNCT
american_scientific_journal-7486	172	1	fprintf	fprintf	NOUN
american_scientific_journal-7486	172	2	(	(	PUNCT
american_scientific_journal-7486	172	3	'	'	PUNCT
american_scientific_journal-7486	172	4	\	\	X
american_scientific_journal-7486	172	5	n	n	CCONJ
american_scientific_journal-7486	172	6	the	the	DET
american_scientific_journal-7486	172	7	given	give	VERB
american_scientific_journal-7486	172	8	number	number	NOUN
american_scientific_journal-7486	172	9	is	be	AUX
american_scientific_journal-7486	172	10	a	a	DET
american_scientific_journal-7486	172	11	candidate	candidate	NOUN
american_scientific_journal-7486	172	12	prime	prime	ADJ
american_scientific_journal-7486	172	13	number	number	NOUN
american_scientific_journal-7486	172	14	'	'	PUNCT
american_scientific_journal-7486	172	15	)	)	PUNCT
american_scientific_journal-7486	172	16	;	;	PUNCT
american_scientific_journal-7486	172	17	else	else	ADV
american_scientific_journal-7486	172	18	fprintf	fprintf	X
american_scientific_journal-7486	172	19	(	(	PUNCT
american_scientific_journal-7486	172	20	'	'	PUNCT
american_scientific_journal-7486	172	21	\	\	X
american_scientific_journal-7486	172	22	n	n	CCONJ
american_scientific_journal-7486	172	23	the	the	DET
american_scientific_journal-7486	172	24	given	give	VERB
american_scientific_journal-7486	172	25	number	number	NOUN
american_scientific_journal-7486	172	26	is	be	AUX
american_scientific_journal-7486	172	27	---not	---not	PUNCT
american_scientific_journal-7486	172	28	--	--	PUNCT
american_scientific_journal-7486	172	29	a	a	DET
american_scientific_journal-7486	172	30	prime	prime	ADJ
american_scientific_journal-7486	172	31	number	number	NOUN
american_scientific_journal-7486	172	32	'	'	PUNCT
american_scientific_journal-7486	172	33	)	)	PUNCT
american_scientific_journal-7486	172	34	;	;	PUNCT
american_scientific_journal-7486	172	35	end	end	VERB
american_scientific_journal-7486	172	36	end	end	NOUN
american_scientific_journal-7486	172	37	appendix	appendix	VERB
american_scientific_journal-7486	172	38	2	2	NUM
american_scientific_journal-7486	172	39	matlab	matlab	PROPN
american_scientific_journal-7486	172	40	code	code	NOUN
american_scientific_journal-7486	172	41	for	for	ADP
american_scientific_journal-7486	172	42	collatz	collatz	NOUN
american_scientific_journal-7486	172	43	conjecture	conjecture	NOUN
american_scientific_journal-7486	172	44	theorem	theorem	VERB
american_scientific_journal-7486	172	45	4.2	4.2	NUM
american_scientific_journal-7486	172	46	.	.	PUNCT
american_scientific_journal-7486	173	1	clc	clc	PROPN
american_scientific_journal-7486	173	2	clear	clear	ADJ
american_scientific_journal-7486	173	3	all	all	DET
american_scientific_journal-7486	173	4	flag	flag	NOUN
american_scientific_journal-7486	173	5	=	=	NOUN
american_scientific_journal-7486	173	6	0	0	NUM
american_scientific_journal-7486	173	7	;	;	PUNCT
american_scientific_journal-7486	173	8	input_no	input_no	NOUN
american_scientific_journal-7486	173	9	=	=	SYM
american_scientific_journal-7486	173	10	input	input	NOUN
american_scientific_journal-7486	173	11	(	(	PUNCT
american_scientific_journal-7486	173	12	'	'	PUNCT
american_scientific_journal-7486	173	13	enter	enter	VERB
american_scientific_journal-7486	173	14	a	a	DET
american_scientific_journal-7486	173	15	prime	prime	ADJ
american_scientific_journal-7486	173	16	number	number	NOUN
american_scientific_journal-7486	173	17	greater	great	ADJ
american_scientific_journal-7486	173	18	than	than	ADP
american_scientific_journal-7486	173	19	three	three	NUM
american_scientific_journal-7486	173	20	'	'	PUNCT
american_scientific_journal-7486	173	21	)	)	PUNCT
american_scientific_journal-7486	173	22	;	;	PUNCT
american_scientific_journal-7486	173	23	if	if	SCONJ
american_scientific_journal-7486	173	24	(	(	PUNCT
american_scientific_journal-7486	173	25	input_no<=1	input_no<=1	PROPN
american_scientific_journal-7486	173	26	||	||	NOUN
american_scientific_journal-7486	173	27	input_no==3	input_no==3	PROPN
american_scientific_journal-7486	173	28	)	)	PUNCT
american_scientific_journal-7486	173	29	fprintf	fprintf	X
american_scientific_journal-7486	173	30	(	(	PUNCT
american_scientific_journal-7486	173	31	'	'	PUNCT
american_scientific_journal-7486	173	32	please	please	INTJ
american_scientific_journal-7486	173	33	enter	enter	VERB
american_scientific_journal-7486	173	34	a	a	DET
american_scientific_journal-7486	173	35	valid	valid	ADJ
american_scientific_journal-7486	173	36	prime	prime	ADJ
american_scientific_journal-7486	173	37	number	number	NOUN
american_scientific_journal-7486	173	38	'	'	PUNCT
american_scientific_journal-7486	173	39	)	)	PUNCT
american_scientific_journal-7486	173	40	;	;	PUNCT
american_scientific_journal-7486	173	41	else	else	ADV
american_scientific_journal-7486	173	42	answer	answer	NOUN
american_scientific_journal-7486	173	43	=	=	PUNCT
american_scientific_journal-7486	173	44	isprime	isprime	NOUN
american_scientific_journal-7486	173	45	(	(	PUNCT
american_scientific_journal-7486	173	46	input_no	input_no	PROPN
american_scientific_journal-7486	173	47	)	)	PUNCT
american_scientific_journal-7486	173	48	;	;	PUNCT
american_scientific_journal-7486	173	49	if	if	SCONJ
american_scientific_journal-7486	173	50	(	(	PUNCT
american_scientific_journal-7486	173	51	answer==1	answer==1	X
american_scientific_journal-7486	173	52	)	)	PUNCT
american_scientific_journal-7486	173	53	y=2*input_no	y=2*input_no	X
american_scientific_journal-7486	173	54	;	;	PUNCT
american_scientific_journal-7486	173	55	fprintf	fprintf	X
american_scientific_journal-7486	173	56	(	(	PUNCT
american_scientific_journal-7486	173	57	'	'	PUNCT
american_scientific_journal-7486	173	58	the	the	DET
american_scientific_journal-7486	173	59	number	number	NOUN
american_scientific_journal-7486	173	60	%	%	NOUN
american_scientific_journal-7486	173	61	d	d	NOUN
american_scientific_journal-7486	173	62	is	be	AUX
american_scientific_journal-7486	173	63	collatz	collatz	NOUN
american_scientific_journal-7486	173	64	number	number	NOUN
american_scientific_journal-7486	173	65	of	of	ADP
american_scientific_journal-7486	173	66	%	%	INTJ
american_scientific_journal-7486	173	67	d	d	NOUN
american_scientific_journal-7486	173	68	'	'	NOUN
american_scientific_journal-7486	173	69	,	,	PUNCT
american_scientific_journal-7486	173	70	input_no	input_no	PROPN
american_scientific_journal-7486	173	71	,	,	PUNCT
american_scientific_journal-7486	173	72	y	y	PROPN
american_scientific_journal-7486	173	73	)	)	PUNCT
american_scientific_journal-7486	173	74	;	;	PUNCT
american_scientific_journal-7486	173	75	else	else	ADV
american_scientific_journal-7486	173	76	american	american	PROPN
american_scientific_journal-7486	173	77	academic	academic	ADJ
american_scientific_journal-7486	173	78	scientific	scientific	ADJ
american_scientific_journal-7486	173	79	research	research	NOUN
american_scientific_journal-7486	173	80	journal	journal	NOUN
american_scientific_journal-7486	173	81	for	for	ADP
american_scientific_journal-7486	173	82	engineering	engineering	NOUN
american_scientific_journal-7486	173	83	,	,	PUNCT
american_scientific_journal-7486	173	84	technology	technology	NOUN
american_scientific_journal-7486	173	85	,	,	PUNCT
american_scientific_journal-7486	173	86	and	and	CCONJ
american_scientific_journal-7486	173	87	sciences	science	NOUN
american_scientific_journal-7486	173	88	(	(	PUNCT
american_scientific_journal-7486	173	89	asrjets	asrjet	NOUN
american_scientific_journal-7486	173	90	)	)	PUNCT
american_scientific_journal-7486	173	91	(	(	PUNCT
american_scientific_journal-7486	173	92	2022	2022	NUM
american_scientific_journal-7486	173	93	)	)	PUNCT
american_scientific_journal-7486	173	94	volume	volume	NOUN
american_scientific_journal-7486	173	95	88	88	NUM
american_scientific_journal-7486	173	96	,	,	PUNCT
american_scientific_journal-7486	173	97	no	no	DET
american_scientific_journal-7486	173	98	1	1	NUM
american_scientific_journal-7486	173	99	,	,	PUNCT
american_scientific_journal-7486	173	100	pp	pp	ADV
american_scientific_journal-7486	173	101	77	77	NUM
american_scientific_journal-7486	173	102	-	-	SYM
american_scientific_journal-7486	173	103	90	90	NUM
american_scientific_journal-7486	173	104	88	88	NUM
american_scientific_journal-7486	173	105	fprintf	fprintf	NOUN
american_scientific_journal-7486	173	106	(	(	PUNCT
american_scientific_journal-7486	173	107	'	'	PUNCT
american_scientific_journal-7486	173	108	the	the	DET
american_scientific_journal-7486	173	109	number	number	NOUN
american_scientific_journal-7486	173	110	is	be	AUX
american_scientific_journal-7486	173	111	not	not	PART
american_scientific_journal-7486	173	112	prime	prime	ADJ
american_scientific_journal-7486	173	113	'	'	PUNCT
american_scientific_journal-7486	173	114	)	)	PUNCT
american_scientific_journal-7486	173	115	;	;	PUNCT
american_scientific_journal-7486	173	116	end	end	VERB
american_scientific_journal-7486	173	117	end	end	NOUN
american_scientific_journal-7486	173	118	appendix	appendix	VERB
american_scientific_journal-7486	173	119	3	3	NUM
american_scientific_journal-7486	173	120	matlab	matlab	PROPN
american_scientific_journal-7486	173	121	code	code	NOUN
american_scientific_journal-7486	173	122	for	for	ADP
american_scientific_journal-7486	173	123	corollary	corollary	ADJ
american_scientific_journal-7486	173	124	4.4	4.4	NUM
american_scientific_journal-7486	173	125	.	.	PUNCT
american_scientific_journal-7486	174	1	c	c	X
american_scientific_journal-7486	175	1	l	l	NOUN
american_scientific_journal-7486	175	2	c	c	NOUN
american_scientific_journal-7486	175	3	c	c	NOUN
american_scientific_journal-7486	175	4	l	l	NOUN
american_scientific_journal-7486	175	5	e	e	X
american_scientific_journal-7486	175	6	a	a	DET
american_scientific_journal-7486	175	7	r	r	NOUN
american_scientific_journal-7486	175	8	a	a	DET
american_scientific_journal-7486	175	9	l	l	NOUN
american_scientific_journal-7486	175	10	l	l	NOUN
american_scientific_journal-7486	175	11	f	f	X
american_scientific_journal-7486	175	12	l	l	NOUN
american_scientific_journal-7486	175	13	a	a	DET
american_scientific_journal-7486	175	14	g	g	NOUN
american_scientific_journal-7486	175	15	=	=	NOUN
american_scientific_journal-7486	175	16	0	0	NUM
american_scientific_journal-7486	175	17	;	;	PUNCT
american_scientific_journal-7486	175	18	input	input	NOUN
american_scientific_journal-7486	175	19	no	no	PRON
american_scientific_journal-7486	176	1	=	=	NOUN
american_scientific_journal-7486	176	2	i	i	PRON
american_scientific_journal-7486	176	3	n	n	NOUN
american_scientific_journal-7486	176	4	p	p	NOUN
american_scientific_journal-7486	176	5	u	u	X
american_scientific_journal-7486	176	6	t	t	X
american_scientific_journal-7486	176	7	(	(	PUNCT
american_scientific_journal-7486	176	8	’	'	PUNCT
american_scientific_journal-7486	176	9	enter	enter	VERB
american_scientific_journal-7486	176	10	a	a	DET
american_scientific_journal-7486	176	11	prime	prime	ADJ
american_scientific_journal-7486	176	12	number	number	NOUN
american_scientific_journal-7486	176	13	g	g	NOUN
american_scientific_journal-7486	176	14	r	r	NOUN
american_scientific_journal-7486	176	15	e	e	NOUN
american_scientific_journal-7486	176	16	a	a	PRON
american_scientific_journal-7486	176	17	t	t	NOUN
american_scientific_journal-7486	176	18	e	e	NOUN
american_scientific_journal-7486	176	19	r	r	NOUN
american_scientific_journal-7486	176	20	than	than	ADP
american_scientific_journal-7486	176	21	30	30	NUM
american_scientific_journal-7486	176	22	’	'	PUNCT
american_scientific_journal-7486	176	23	)	)	PUNCT
american_scientific_journal-7486	177	1	;	;	PUNCT
american_scientific_journal-7486	177	2	i	i	PRON
american_scientific_journal-7486	177	3	f	f	X
american_scientific_journal-7486	177	4	(	(	PUNCT
american_scientific_journal-7486	177	5	input	input	VERB
american_scientific_journal-7486	177	6	no	no	PRON
american_scientific_journal-7486	177	7	<	<	NOUN
american_scientific_journal-7486	177	8	30	30	NUM
american_scientific_journal-7486	177	9	)	)	PUNCT
american_scientific_journal-7486	178	1	f	f	PROPN
american_scientific_journal-7486	179	1	p	p	NOUN
american_scientific_journal-7486	179	2	r	r	NOUN
american_scientific_journal-7486	180	1	i	i	PRON
american_scientific_journal-7486	180	2	n	n	VERB
american_scientific_journal-7486	180	3	t	t	PROPN
american_scientific_journal-7486	180	4	f	f	PROPN
american_scientific_journal-7486	180	5	(	(	PUNCT
american_scientific_journal-7486	180	6	’	'	PUNCT
american_scientific_journal-7486	180	7	pl	pl	X
american_scientific_journal-7486	180	8	e	e	PROPN
american_scientific_journal-7486	180	9	a	a	DET
american_scientific_journal-7486	180	10	s	s	X
american_scientific_journal-7486	180	11	e	e	NOUN
american_scientific_journal-7486	180	12	e	e	NOUN
american_scientific_journal-7486	180	13	n	n	NOUN
american_scientific_journal-7486	180	14	t	t	X
american_scientific_journal-7486	180	15	e	e	X
american_scientific_journal-7486	180	16	r	r	NOUN
american_scientific_journal-7486	180	17	a	a	DET
american_scientific_journal-7486	180	18	prime	prime	ADJ
american_scientific_journal-7486	180	19	number	number	NOUN
american_scientific_journal-7486	180	20	g	g	NOUN
american_scientific_journal-7486	180	21	r	r	NOUN
american_scientific_journal-7486	180	22	e	e	NOUN
american_scientific_journal-7486	180	23	a	a	PRON
american_scientific_journal-7486	180	24	t	t	NOUN
american_scientific_journal-7486	180	25	e	e	NOUN
american_scientific_journal-7486	180	26	r	r	NOUN
american_scientific_journal-7486	180	27	than	than	ADP
american_scientific_journal-7486	180	28	30	30	NUM
american_scientific_journal-7486	180	29	’	'	PUNCT
american_scientific_journal-7486	180	30	)	)	PUNCT
american_scientific_journal-7486	181	1	;	;	PUNCT
american_scientific_journal-7486	181	2	e	e	X
american_scientific_journal-7486	181	3	l	l	NOUN
american_scientific_journal-7486	181	4	s	s	PART
american_scientific_journal-7486	181	5	e	e	NOUN
american_scientific_journal-7486	181	6	answer	answer	NOUN
american_scientific_journal-7486	181	7	=	=	PUNCT
american_scientific_journal-7486	181	8	isprime	isprime	NOUN
american_scientific_journal-7486	181	9	(	(	PUNCT
american_scientific_journal-7486	181	10	input	input	NOUN
american_scientific_journal-7486	181	11	no	no	INTJ
american_scientific_journal-7486	181	12	)	)	PUNCT
american_scientific_journal-7486	181	13	;	;	PUNCT
american_scientific_journal-7486	182	1	i	i	PRON
american_scientific_journal-7486	182	2	f	f	X
american_scientific_journal-7486	182	3	(	(	PUNCT
american_scientific_journal-7486	182	4	answer==1	answer==1	NOUN
american_scientific_journal-7486	182	5	)	)	PUNCT
american_scientific_journal-7486	182	6	r=[1	r=[1	NOUN
american_scientific_journal-7486	182	7	,	,	PUNCT
american_scientific_journal-7486	182	8	6	6	NUM
american_scientific_journal-7486	182	9	,	,	PUNCT
american_scientific_journal-7486	182	10	4	4	NUM
american_scientific_journal-7486	182	11	,	,	PUNCT
american_scientific_journal-7486	182	12	2	2	NUM
american_scientific_journal-7486	182	13	,	,	PUNCT
american_scientific_journal-7486	182	14	4	4	NUM
american_scientific_journal-7486	182	15	,	,	PUNCT
american_scientific_journal-7486	182	16	2	2	NUM
american_scientific_journal-7486	182	17	,	,	PUNCT
american_scientific_journal-7486	182	18	4	4	NUM
american_scientific_journal-7486	182	19	,	,	PUNCT
american_scientific_journal-7486	182	20	6	6	NUM
american_scientific_journal-7486	182	21	]	]	PUNCT
american_scientific_journal-7486	182	22	;	;	PUNCT
american_scientific_journal-7486	182	23	a	a	DET
american_scientific_journal-7486	182	24	=	=	NOUN
american_scientific_journal-7486	182	25	input	input	NOUN
american_scientific_journal-7486	182	26	no	no	PRON
american_scientific_journal-7486	182	27	/	/	SYM
american_scientific_journal-7486	182	28	30	30	NUM
american_scientific_journal-7486	182	29	;	;	PUNCT
american_scientific_journal-7486	182	30	t=	t=	NOUN
american_scientific_journal-7486	182	31	f	f	X
american_scientific_journal-7486	182	32	l	l	NOUN
american_scientific_journal-7486	183	1	o	o	X
american_scientific_journal-7486	183	2	o	o	X
american_scientific_journal-7486	183	3	r	r	NOUN
american_scientific_journal-7486	183	4	(	(	PUNCT
american_scientific_journal-7486	183	5	a	a	NOUN
american_scientific_journal-7486	183	6	)	)	PUNCT
american_scientific_journal-7486	183	7	;	;	PUNCT
american_scientific_journal-7486	183	8	x1=30∗	x1=30∗	PROPN
american_scientific_journal-7486	183	9	t	t	PROPN
american_scientific_journal-7486	183	10	;	;	PUNCT
american_scientific_journal-7486	183	11	s	s	X
american_scientific_journal-7486	183	12	=	=	X
american_scientific_journal-7486	183	13	x1	x1	PROPN
american_scientific_journal-7486	183	14	;	;	PUNCT
american_scientific_journal-7486	183	15	f	f	PROPN
american_scientific_journal-7486	183	16	=	=	PROPN
american_scientific_journal-7486	183	17	0	0	NUM
american_scientific_journal-7486	183	18	;	;	PUNCT
american_scientific_journal-7486	183	19	j	j	PROPN
american_scientific_journal-7486	183	20	=	=	PROPN
american_scientific_journal-7486	183	21	1	1	NUM
american_scientific_journal-7486	183	22	;	;	PUNCT
american_scientific_journal-7486	183	23	american	american	ADJ
american_scientific_journal-7486	183	24	academic	academic	ADJ
american_scientific_journal-7486	183	25	scientific	scientific	ADJ
american_scientific_journal-7486	183	26	research	research	NOUN
american_scientific_journal-7486	183	27	journal	journal	NOUN
american_scientific_journal-7486	183	28	for	for	ADP
american_scientific_journal-7486	183	29	engineering	engineering	NOUN
american_scientific_journal-7486	183	30	,	,	PUNCT
american_scientific_journal-7486	183	31	technology	technology	NOUN
american_scientific_journal-7486	183	32	,	,	PUNCT
american_scientific_journal-7486	183	33	and	and	CCONJ
american_scientific_journal-7486	183	34	sciences	science	NOUN
american_scientific_journal-7486	183	35	(	(	PUNCT
american_scientific_journal-7486	183	36	asrjets	asrjet	NOUN
american_scientific_journal-7486	183	37	)	)	PUNCT
american_scientific_journal-7486	183	38	(	(	PUNCT
american_scientific_journal-7486	183	39	2022	2022	NUM
american_scientific_journal-7486	183	40	)	)	PUNCT
american_scientific_journal-7486	183	41	volume	volume	NOUN
american_scientific_journal-7486	183	42	88	88	NUM
american_scientific_journal-7486	183	43	,	,	PUNCT
american_scientific_journal-7486	183	44	no	no	DET
american_scientific_journal-7486	183	45	1	1	NUM
american_scientific_journal-7486	183	46	,	,	PUNCT
american_scientific_journal-7486	183	47	pp	pp	ADV
american_scientific_journal-7486	183	48	77	77	NUM
american_scientific_journal-7486	183	49	-	-	SYM
american_scientific_journal-7486	183	50	90	90	NUM
american_scientific_journal-7486	183	51	89	89	NUM
american_scientific_journal-7486	183	52	f	f	NOUN
american_scientific_journal-7486	183	53	o	o	NOUN
american_scientific_journal-7486	183	54	r	r	NOUN
american_scientific_journal-7486	183	55	i	i	NOUN
american_scientific_journal-7486	183	56	=	=	VERB
american_scientific_journal-7486	183	57	1:8	1:8	NUM
american_scientific_journal-7486	184	1	i	i	NOUN
american_scientific_journal-7486	184	2	f	f	PROPN
american_scientific_journal-7486	184	3	(	(	PUNCT
american_scientific_journal-7486	184	4	input	input	NOUN
american_scientific_journal-7486	184	5	no==s	no==s	PROPN
american_scientific_journal-7486	184	6	)	)	PUNCT
american_scientific_journal-7486	184	7	f	f	PROPN
american_scientific_journal-7486	185	1	=	=	SYM
american_scientific_journal-7486	185	2	1	1	NUM
american_scientific_journal-7486	185	3	;	;	PUNCT
american_scientific_journal-7486	185	4	break	break	NOUN
american_scientific_journal-7486	185	5	;	;	PUNCT
american_scientific_journal-7486	185	6	e	e	X
american_scientific_journal-7486	185	7	l	l	NOUN
american_scientific_journal-7486	185	8	s	s	PART
american_scientific_journal-7486	185	9	e	e	X
american_scientific_journal-7486	185	10	s	s	PROPN
american_scientific_journal-7486	185	11	=	=	SYM
american_scientific_journal-7486	185	12	s+r	s+r	X
american_scientific_journal-7486	185	13	(	(	PUNCT
american_scientific_journal-7486	185	14	1	1	NUM
american_scientific_journal-7486	185	15	,	,	PUNCT
american_scientific_journal-7486	185	16	i	i	PROPN
american_scientific_journal-7486	185	17	)	)	PUNCT
american_scientific_journal-7486	185	18	;	;	PUNCT
american_scientific_journal-7486	186	1	c	c	X
american_scientific_journal-7486	186	2	(	(	PUNCT
american_scientific_journal-7486	186	3	1	1	NUM
american_scientific_journal-7486	186	4	,	,	PUNCT
american_scientific_journal-7486	186	5	j	j	NOUN
american_scientific_journal-7486	186	6	)	)	PUNCT
american_scientific_journal-7486	186	7	=	=	SYM
american_scientific_journal-7486	186	8	r	r	NOUN
american_scientific_journal-7486	186	9	(	(	PUNCT
american_scientific_journal-7486	186	10	1	1	NUM
american_scientific_journal-7486	186	11	,	,	PUNCT
american_scientific_journal-7486	186	12	i	i	PROPN
american_scientific_journal-7486	186	13	)	)	PUNCT
american_scientific_journal-7486	186	14	;	;	PUNCT
american_scientific_journal-7486	187	1	j	j	PROPN
american_scientific_journal-7486	187	2	=	=	PROPN
american_scientific_journal-7486	187	3	j	j	PROPN
american_scientific_journal-7486	187	4	+1	+1	PROPN
american_scientific_journal-7486	187	5	;	;	PUNCT
american_scientific_journal-7486	187	6	i	i	PRON
american_scientific_journal-7486	187	7	f	f	X
american_scientific_journal-7486	188	1	(	(	PUNCT
american_scientific_journal-7486	188	2	i	i	PRON
american_scientific_journal-7486	188	3	=	=	PROPN
american_scientific_journal-7486	188	4	=	=	PROPN
american_scientific_journal-7486	188	5	8)	8)	NUM
american_scientific_journal-7486	188	6	f	f	NOUN
american_scientific_journal-7486	188	7	=	=	PROPN
american_scientific_journal-7486	188	8	1	1	NUM
american_scientific_journal-7486	188	9	;	;	PUNCT
american_scientific_journal-7486	188	10	end	end	VERB
american_scientific_journal-7486	188	11	end	end	NOUN
american_scientific_journal-7486	188	12	end	end	NOUN
american_scientific_journal-7486	188	13	[	[	PUNCT
american_scientific_journal-7486	188	14	row	row	NOUN
american_scientific_journal-7486	188	15	,	,	PUNCT
american_scientific_journal-7486	188	16	col]=	col]=	ADV
american_scientific_journal-7486	188	17	s	s	VERB
american_scientific_journal-7486	188	18	i	i	PRON
american_scientific_journal-7486	188	19	z	z	NOUN
american_scientific_journal-7486	188	20	e	e	X
american_scientific_journal-7486	188	21	(	(	PUNCT
american_scientific_journal-7486	188	22	c	c	PROPN
american_scientific_journal-7486	188	23	)	)	PUNCT
american_scientific_journal-7486	188	24	;	;	PUNCT
american_scientific_journal-7486	189	1	i	i	PRON
american_scientific_journal-7486	189	2	f	f	X
american_scientific_journal-7486	190	1	(	(	PUNCT
american_scientific_journal-7486	190	2	f	f	PROPN
american_scientific_journal-7486	190	3	=	=	NOUN
american_scientific_journal-7486	190	4	=	=	NOUN
american_scientific_journal-7486	190	5	1	1	NUM
american_scientific_journal-7486	190	6	)	)	PUNCT
american_scientific_journal-7486	191	1	f	f	NOUN
american_scientific_journal-7486	192	1	p	p	NOUN
american_scientific_journal-7486	192	2	r	r	NOUN
american_scientific_journal-7486	192	3	i	i	PRON
american_scientific_journal-7486	192	4	n	n	VERB
american_scientific_journal-7486	192	5	t	t	PROPN
american_scientific_journal-7486	192	6	f	f	PROPN
american_scientific_journal-7486	192	7	(	(	PUNCT
american_scientific_journal-7486	192	8	’	'	PUNCT
american_scientific_journal-7486	192	9	%	%	NOUN
american_scientific_journal-7486	193	1	d	d	X
american_scientific_journal-7486	193	2	=	=	SYM
american_scientific_journal-7486	194	1	%	%	INTJ
american_scientific_journal-7486	194	2	d	d	X
american_scientific_journal-7486	194	3	+	+	CCONJ
american_scientific_journal-7486	194	4	(	(	PUNCT
american_scientific_journal-7486	194	5	’	'	PUNCT
american_scientific_journal-7486	194	6	,	,	PUNCT
american_scientific_journal-7486	194	7	input	input	VERB
american_scientific_journal-7486	194	8	no	no	INTJ
american_scientific_journal-7486	194	9	,	,	PUNCT
american_scientific_journal-7486	194	10	x1	x1	PROPN
american_scientific_journal-7486	194	11	)	)	PUNCT
american_scientific_journal-7486	195	1	f	f	NOUN
american_scientific_journal-7486	196	1	o	o	NOUN
american_scientific_journal-7486	196	2	r	r	NOUN
american_scientific_journal-7486	196	3	k=1	k=1	NOUN
american_scientific_journal-7486	196	4	:	:	PUNCT
american_scientific_journal-7486	196	5	col	col	PROPN
american_scientific_journal-7486	197	1	i	i	PRON
american_scientific_journal-7486	197	2	f	f	PROPN
american_scientific_journal-7486	198	1	(	(	PUNCT
american_scientific_journal-7486	198	2	k==col	k==col	PROPN
american_scientific_journal-7486	198	3	)	)	PUNCT
american_scientific_journal-7486	199	1	f	f	PROPN
american_scientific_journal-7486	200	1	p	p	NOUN
american_scientific_journal-7486	200	2	r	r	X
american_scientific_journal-7486	201	1	i	i	PRON
american_scientific_journal-7486	201	2	n	n	VERB
american_scientific_journal-7486	201	3	t	t	PROPN
american_scientific_journal-7486	201	4	f	f	PROPN
american_scientific_journal-7486	201	5	(	(	PUNCT
american_scientific_journal-7486	201	6	’	'	PUNCT
american_scientific_journal-7486	201	7	%	%	INTJ
american_scientific_journal-7486	201	8	d	d	NOUN
american_scientific_journal-7486	201	9	)	)	PUNCT
american_scientific_journal-7486	201	10	’	'	PUNCT
american_scientific_journal-7486	201	11	,	,	PUNCT
american_scientific_journal-7486	201	12	c	c	X
american_scientific_journal-7486	201	13	(	(	PUNCT
american_scientific_journal-7486	201	14	k	k	NOUN
american_scientific_journal-7486	201	15	)	)	PUNCT
american_scientific_journal-7486	201	16	)	)	PUNCT
american_scientific_journal-7486	202	1	e	e	X
american_scientific_journal-7486	202	2	l	l	NOUN
american_scientific_journal-7486	202	3	s	s	X
american_scientific_journal-7486	202	4	e	e	X
american_scientific_journal-7486	202	5	f	f	NOUN
american_scientific_journal-7486	202	6	p	p	NOUN
american_scientific_journal-7486	202	7	r	r	NOUN
american_scientific_journal-7486	202	8	i	i	PRON
american_scientific_journal-7486	202	9	n	n	VERB
american_scientific_journal-7486	202	10	t	t	PROPN
american_scientific_journal-7486	202	11	f	f	PROPN
american_scientific_journal-7486	202	12	(	(	PUNCT
american_scientific_journal-7486	202	13	’	'	PUNCT
american_scientific_journal-7486	202	14	%	%	INTJ
american_scientific_journal-7486	203	1	d	d	X
american_scientific_journal-7486	203	2	+	+	CCONJ
american_scientific_journal-7486	203	3	’	'	PUNCT
american_scientific_journal-7486	203	4	,	,	PUNCT
american_scientific_journal-7486	203	5	c	c	X
american_scientific_journal-7486	203	6	(	(	PUNCT
american_scientific_journal-7486	203	7	k	k	NOUN
american_scientific_journal-7486	203	8	)	)	PUNCT
american_scientific_journal-7486	203	9	)	)	PUNCT
american_scientific_journal-7486	203	10	end	end	VERB
american_scientific_journal-7486	203	11	american	american	ADJ
american_scientific_journal-7486	203	12	academic	academic	ADJ
american_scientific_journal-7486	203	13	scientific	scientific	ADJ
american_scientific_journal-7486	203	14	research	research	NOUN
american_scientific_journal-7486	203	15	journal	journal	NOUN
american_scientific_journal-7486	203	16	for	for	ADP
american_scientific_journal-7486	203	17	engineering	engineering	NOUN
american_scientific_journal-7486	203	18	,	,	PUNCT
american_scientific_journal-7486	203	19	technology	technology	NOUN
american_scientific_journal-7486	203	20	,	,	PUNCT
american_scientific_journal-7486	203	21	and	and	CCONJ
american_scientific_journal-7486	203	22	sciences	science	NOUN
american_scientific_journal-7486	203	23	(	(	PUNCT
american_scientific_journal-7486	203	24	asrjets	asrjet	NOUN
american_scientific_journal-7486	203	25	)	)	PUNCT
american_scientific_journal-7486	203	26	(	(	PUNCT
american_scientific_journal-7486	203	27	2022	2022	NUM
american_scientific_journal-7486	203	28	)	)	PUNCT
american_scientific_journal-7486	203	29	volume	volume	NOUN
american_scientific_journal-7486	203	30	88	88	NUM
american_scientific_journal-7486	203	31	,	,	PUNCT
american_scientific_journal-7486	203	32	no	no	DET
american_scientific_journal-7486	203	33	1	1	NUM
american_scientific_journal-7486	203	34	,	,	PUNCT
american_scientific_journal-7486	203	35	pp	pp	ADV
american_scientific_journal-7486	203	36	77	77	NUM
american_scientific_journal-7486	203	37	-	-	SYM
american_scientific_journal-7486	203	38	90	90	NUM
american_scientific_journal-7486	203	39	90	90	NUM
american_scientific_journal-7486	203	40	end	end	NOUN
american_scientific_journal-7486	203	41	end	end	NOUN
american_scientific_journal-7486	204	1	e	e	X
american_scientific_journal-7486	204	2	l	l	NOUN
american_scientific_journal-7486	204	3	s	s	X
american_scientific_journal-7486	204	4	e	e	X
american_scientific_journal-7486	204	5	f	f	NOUN
american_scientific_journal-7486	204	6	p	p	NOUN
american_scientific_journal-7486	204	7	r	r	NOUN
american_scientific_journal-7486	205	1	i	i	PRON
american_scientific_journal-7486	206	1	n	n	VERB
american_scientific_journal-7486	206	2	t	t	PROPN
american_scientific_journal-7486	206	3	f	f	PROPN
american_scientific_journal-7486	206	4	(	(	PUNCT
american_scientific_journal-7486	206	5	’	'	PUNCT
american_scientific_journal-7486	206	6	pl	pl	X
american_scientific_journal-7486	206	7	e	e	PROPN
american_scientific_journal-7486	206	8	a	a	DET
american_scientific_journal-7486	206	9	s	s	X
american_scientific_journal-7486	206	10	e	e	NOUN
american_scientific_journal-7486	206	11	e	e	NOUN
american_scientific_journal-7486	206	12	n	n	NOUN
american_scientific_journal-7486	206	13	t	t	X
american_scientific_journal-7486	206	14	e	e	X
american_scientific_journal-7486	206	15	r	r	NOUN
american_scientific_journal-7486	206	16	a	a	DET
american_scientific_journal-7486	206	17	v	v	NOUN
american_scientific_journal-7486	206	18	a	a	DET
american_scientific_journal-7486	206	19	l	l	NOUN
american_scientific_journal-7486	207	1	i	i	NOUN
american_scientific_journal-7486	207	2	d	d	NOUN
american_scientific_journal-7486	207	3	prime	prime	ADJ
american_scientific_journal-7486	207	4	number	number	NOUN
american_scientific_journal-7486	207	5	g	g	NOUN
american_scientific_journal-7486	207	6	r	r	NOUN
american_scientific_journal-7486	207	7	e	e	NOUN
american_scientific_journal-7486	207	8	a	a	PRON
american_scientific_journal-7486	207	9	t	t	NOUN
american_scientific_journal-7486	207	10	e	e	NOUN
american_scientific_journal-7486	207	11	r	r	NOUN
american_scientific_journal-7486	207	12	than	than	ADP
american_scientific_journal-7486	207	13	3	3	NUM
american_scientific_journal-7486	207	14	0	0	NUM
american_scientific_journal-7486	207	15	’	'	PUNCT
american_scientific_journal-7486	207	16	)	)	PUNCT
american_scientific_journal-7486	207	17	;	;	PUNCT
american_scientific_journal-7486	207	18	end	end	VERB
american_scientific_journal-7486	207	19	end	end	NOUN