id	sid	tid	token	lemma	pos
stem-4332	1	1	290	290	NUM
stem-4332	1	2	journal	journal	NOUN
stem-4332	1	3	of	of	ADP
stem-4332	1	4	language	language	NOUN
stem-4332	1	5	,	,	PUNCT
stem-4332	1	6	literacy	literacy	NOUN
stem-4332	1	7	and	and	CCONJ
stem-4332	1	8	learning	learn	VERB
stem-4332	1	9	in	in	ADP
stem-4332	1	10	stem	stem	NOUN
stem-4332	1	11	education	education	NOUN
stem-4332	1	12	www	www	PROPN
stem-4332	1	13	.	.	PROPN
stem-4332	2	1	grnjournal.us	grnjournal.us	PROPN
stem-4332	2	2	american	american	PROPN
stem-4332	2	3	journal	journal	PROPN
stem-4332	2	4	of	of	ADP
stem-4332	2	5	language	language	NOUN
stem-4332	2	6	,	,	PUNCT
stem-4332	2	7	literacy	literacy	NOUN
stem-4332	2	8	and	and	CCONJ
stem-4332	2	9	learning	learn	VERB
stem-4332	2	10	in	in	ADP
stem-4332	2	11	stem	stem	NOUN
stem-4332	2	12	education	education	NOUN
stem-4332	2	13	volume	volume	NOUN
stem-4332	2	14	02	02	NUM
stem-4332	2	15	,	,	PUNCT
stem-4332	2	16	issue	issue	NOUN
stem-4332	2	17	04	04	NUM
stem-4332	2	18	,	,	PUNCT
stem-4332	2	19	2024	2024	NUM
stem-4332	2	20	issn	issn	X
stem-4332	2	21	(	(	PUNCT
stem-4332	2	22	e	e	NOUN
stem-4332	2	23	):	):	PUNCT
stem-4332	2	24	2993	2993	NUM
stem-4332	2	25	-	-	SYM
stem-4332	2	26	2769	2769	NUM
stem-4332	2	27	the	the	DET
stem-4332	2	28	existence	existence	NOUN
stem-4332	2	29	of	of	ADP
stem-4332	2	30	odd	odd	ADJ
stem-4332	2	31	perfect	perfect	ADJ
stem-4332	2	32	numbers	number	NOUN
stem-4332	2	33	zafar	zafar	PROPN
stem-4332	2	34	karimov	karimov	PROPN
stem-4332	2	35	student	student	NOUN
stem-4332	2	36	of	of	ADP
stem-4332	2	37	the	the	DET
stem-4332	2	38	physics	physics	NOUN
stem-4332	2	39	and	and	CCONJ
stem-4332	2	40	mathematics	mathematic	NOUN
stem-4332	2	41	faculty	faculty	NOUN
stem-4332	2	42	of	of	ADP
stem-4332	2	43	termez	termez	PROPN
stem-4332	2	44	state	state	PROPN
stem-4332	2	45	university	university	PROPN
stem-4332	2	46	abstract	abstract	NOUN
stem-4332	2	47	:	:	PUNCT
stem-4332	2	48	this	this	DET
stem-4332	2	49	paper	paper	NOUN
stem-4332	2	50	is	be	AUX
stem-4332	2	51	devoted	devote	VERB
stem-4332	2	52	to	to	ADP
stem-4332	2	53	the	the	DET
stem-4332	2	54	history	history	NOUN
stem-4332	2	55	of	of	ADP
stem-4332	2	56	the	the	DET
stem-4332	2	57	problem	problem	NOUN
stem-4332	2	58	of	of	ADP
stem-4332	2	59	existence	existence	NOUN
stem-4332	2	60	of	of	ADP
stem-4332	2	61	odd	odd	ADJ
stem-4332	2	62	perfect	perfect	ADJ
stem-4332	2	63	numbers	number	NOUN
stem-4332	2	64	,	,	PUNCT
stem-4332	2	65	the	the	DET
stem-4332	2	66	oldest	old	ADJ
stem-4332	2	67	unsolved	unsolved	ADJ
stem-4332	2	68	mathematical	mathematical	ADJ
stem-4332	2	69	problem	problem	NOUN
stem-4332	2	70	.	.	PUNCT
stem-4332	3	1	keywords	keyword	NOUN
stem-4332	3	2	:	:	PUNCT
stem-4332	3	3	number	number	NOUN
stem-4332	3	4	,	,	PUNCT
stem-4332	3	5	perfect	perfect	ADJ
stem-4332	3	6	number	number	NOUN
stem-4332	3	7	,	,	PUNCT
stem-4332	3	8	prime	prime	NOUN
stem-4332	3	9	,	,	PUNCT
stem-4332	3	10	odd	odd	ADJ
stem-4332	3	11	,	,	PUNCT
stem-4332	3	12	equal	equal	ADJ
stem-4332	3	13	,	,	PUNCT
stem-4332	3	14	problem	problem	NOUN
stem-4332	3	15	,	,	PUNCT
stem-4332	3	16	sum	sum	NOUN
stem-4332	3	17	,	,	PUNCT
stem-4332	3	18	divisors	divisor	NOUN
stem-4332	3	19	,	,	PUNCT
stem-4332	3	20	integer	integer	NOUN
stem-4332	3	21	,	,	PUNCT
stem-4332	3	22	triangle	triangle	NOUN
stem-4332	3	23	,	,	PUNCT
stem-4332	3	24	binary	binary	NOUN
stem-4332	3	25	,	,	PUNCT
stem-4332	3	26	sigma	sigma	PROPN
stem-4332	3	27	function	function	PROPN
stem-4332	3	28	,	,	PUNCT
stem-4332	3	29	divisors	divisor	NOUN
stem-4332	3	30	function	function	VERB
stem-4332	3	31	,	,	PUNCT
stem-4332	3	32	marsenne	marsenne	NOUN
stem-4332	3	33	primes	prime	NOUN
stem-4332	3	34	.	.	PUNCT
stem-4332	4	1	introduction	introduction	NOUN
stem-4332	4	2	the	the	DET
stem-4332	4	3	problem	problem	NOUN
stem-4332	4	4	of	of	ADP
stem-4332	4	5	the	the	DET
stem-4332	4	6	existence	existence	NOUN
stem-4332	4	7	of	of	ADP
stem-4332	4	8	odd	odd	ADJ
stem-4332	4	9	perfect	perfect	ADJ
stem-4332	4	10	numbers	number	NOUN
stem-4332	4	11	is	be	AUX
stem-4332	4	12	the	the	DET
stem-4332	4	13	oldest	old	ADJ
stem-4332	4	14	unsolved	unsolved	ADJ
stem-4332	4	15	mathematical	mathematical	ADJ
stem-4332	4	16	problem	problem	NOUN
stem-4332	4	17	,	,	PUNCT
stem-4332	4	18	which	which	PRON
stem-4332	4	19	is	be	AUX
stem-4332	4	20	already	already	ADV
stem-4332	4	21	2000	2000	NUM
stem-4332	4	22	years	year	NOUN
stem-4332	4	23	old	old	ADJ
stem-4332	4	24	.	.	PUNCT
stem-4332	5	1	some	some	PRON
stem-4332	5	2	of	of	ADP
stem-4332	5	3	the	the	DET
stem-4332	5	4	brightest	bright	ADJ
stem-4332	5	5	mathematicians	mathematician	NOUN
stem-4332	5	6	of	of	ADP
stem-4332	5	7	all	all	DET
stem-4332	5	8	time	time	NOUN
stem-4332	5	9	like	like	ADP
stem-4332	5	10	nicomachus	nicomachus	NOUN
stem-4332	5	11	,	,	PUNCT
stem-4332	5	12	fermat	fermat	PROPN
stem-4332	5	13	,	,	PUNCT
stem-4332	5	14	marsenne	marsenne	NOUN
stem-4332	5	15	and	and	CCONJ
stem-4332	5	16	euler	euler	NOUN
stem-4332	5	17	have	have	AUX
stem-4332	5	18	tried	try	VERB
stem-4332	5	19	to	to	PART
stem-4332	5	20	solve	solve	VERB
stem-4332	5	21	it	it	PRON
stem-4332	5	22	,	,	PUNCT
stem-4332	5	23	but	but	CCONJ
stem-4332	5	24	all	all	PRON
stem-4332	5	25	of	of	ADP
stem-4332	5	26	them	they	PRON
stem-4332	5	27	failed	fail	VERB
stem-4332	5	28	.	.	PUNCT
stem-4332	6	1	solving	solve	VERB
stem-4332	6	2	this	this	DET
stem-4332	6	3	problem	problem	NOUN
stem-4332	6	4	can	can	AUX
stem-4332	6	5	be	be	AUX
stem-4332	6	6	as	as	ADV
stem-4332	6	7	simple	simple	ADJ
stem-4332	6	8	as	as	ADP
stem-4332	6	9	finding	find	VERB
stem-4332	6	10	a	a	DET
stem-4332	6	11	single	single	ADJ
stem-4332	6	12	number	number	NOUN
stem-4332	6	13	.	.	PUNCT
stem-4332	7	1	in	in	ADP
stem-4332	7	2	the	the	DET
stem-4332	7	3	middle	middle	NOUN
stem-4332	7	4	of	of	ADP
stem-4332	7	5	the	the	DET
stem-4332	7	6	20th	20th	ADJ
stem-4332	7	7	century	century	NOUN
stem-4332	7	8	mathematicians	mathematician	NOUN
stem-4332	7	9	have	have	AUX
stem-4332	7	10	used	use	VERB
stem-4332	7	11	computers	computer	NOUN
stem-4332	7	12	and	and	CCONJ
stem-4332	7	13	checked	check	VERB
stem-4332	7	14	numbers	number	NOUN
stem-4332	7	15	up	up	ADP
stem-4332	7	16	to	to	PART
stem-4332	7	17	10	10	NUM
stem-4332	7	18	to	to	ADP
stem-4332	7	19	the	the	DET
stem-4332	7	20	power	power	NOUN
stem-4332	7	21	of	of	ADP
stem-4332	7	22	2200	2200	NUM
stem-4332	7	23	,	,	PUNCT
stem-4332	7	24	but	but	CCONJ
stem-4332	7	25	so	so	ADV
stem-4332	7	26	far	far	ADV
stem-4332	7	27	they	they	PRON
stem-4332	7	28	have	have	AUX
stem-4332	7	29	been	be	AUX
stem-4332	7	30	unsuccessful	unsuccessful	ADJ
stem-4332	7	31	.	.	PUNCT
stem-4332	8	1	this	this	DET
stem-4332	8	2	problem	problem	NOUN
stem-4332	8	3	has	have	AUX
stem-4332	8	4	captured	capture	VERB
stem-4332	8	5	the	the	DET
stem-4332	8	6	imaginations	imagination	NOUN
stem-4332	8	7	of	of	ADP
stem-4332	8	8	so	so	ADV
stem-4332	8	9	many	many	ADJ
stem-4332	8	10	mathematicians	mathematician	NOUN
stem-4332	8	11	because	because	SCONJ
stem-4332	8	12	it	it	PRON
stem-4332	8	13	's	be	AUX
stem-4332	8	14	old	old	ADJ
stem-4332	8	15	,	,	PUNCT
stem-4332	8	16	it	it	PRON
stem-4332	8	17	's	be	AUX
stem-4332	8	18	simple	simple	ADJ
stem-4332	8	19	and	and	CCONJ
stem-4332	8	20	it	it	PRON
stem-4332	8	21	's	be	AUX
stem-4332	8	22	beautiful	beautiful	ADJ
stem-4332	8	23	.	.	PUNCT
stem-4332	9	1	perfect	perfect	ADJ
stem-4332	9	2	numbers	number	NOUN
stem-4332	9	3	let	let	VERB
stem-4332	9	4	’s	’s	PRON
stem-4332	9	5	take	take	VERB
stem-4332	9	6	the	the	DET
stem-4332	9	7	number	number	NOUN
stem-4332	9	8	six	six	NUM
stem-4332	9	9	.	.	PUNCT
stem-4332	10	1	we	we	PRON
stem-4332	10	2	can	can	AUX
stem-4332	10	3	divide	divide	VERB
stem-4332	10	4	it	it	PRON
stem-4332	10	5	by	by	ADP
stem-4332	10	6	1	1	NUM
stem-4332	10	7	,	,	PUNCT
stem-4332	10	8	2	2	NUM
stem-4332	10	9	and	and	CCONJ
stem-4332	10	10	3	3	NUM
stem-4332	10	11	.	.	PUNCT
stem-4332	11	1	if	if	SCONJ
stem-4332	11	2	we	we	PRON
stem-4332	11	3	add	add	VERB
stem-4332	11	4	up	up	ADP
stem-4332	11	5	all	all	DET
stem-4332	11	6	these	these	DET
stem-4332	11	7	divisors	divisor	NOUN
stem-4332	11	8	,	,	PUNCT
stem-4332	11	9	we	we	PRON
stem-4332	11	10	find	find	VERB
stem-4332	11	11	that	that	SCONJ
stem-4332	11	12	they	they	PRON
stem-4332	11	13	add	add	VERB
stem-4332	11	14	up	up	ADP
stem-4332	11	15	to	to	PART
stem-4332	11	16	six	six	NUM
stem-4332	11	17	,	,	PUNCT
stem-4332	11	18	which	which	PRON
stem-4332	11	19	is	be	AUX
stem-4332	11	20	the	the	DET
stem-4332	11	21	number	number	NOUN
stem-4332	11	22	itself	itself	PRON
stem-4332	11	23	.	.	PUNCT
stem-4332	12	1	numbers	number	NOUN
stem-4332	12	2	like	like	ADP
stem-4332	12	3	this	this	PRON
stem-4332	12	4	are	be	AUX
stem-4332	12	5	perfect	perfect	ADJ
stem-4332	12	6	.	.	PUNCT
stem-4332	13	1	we	we	PRON
stem-4332	13	2	can	can	AUX
stem-4332	13	3	also	also	ADV
stem-4332	13	4	try	try	VERB
stem-4332	13	5	this	this	PRON
stem-4332	13	6	with	with	ADP
stem-4332	13	7	other	other	ADJ
stem-4332	13	8	numbers	number	NOUN
stem-4332	13	9	like	like	ADP
stem-4332	13	10	24	24	NUM
stem-4332	13	11	.	.	NOUN
stem-4332	13	12	24	24	NUM
stem-4332	13	13	has	have	VERB
stem-4332	13	14	the	the	DET
stem-4332	13	15	divisors	divisor	NOUN
stem-4332	13	16	1	1	NUM
stem-4332	13	17	,	,	PUNCT
stem-4332	13	18	2	2	NUM
stem-4332	13	19	,	,	PUNCT
stem-4332	13	20	3	3	NUM
stem-4332	13	21	,	,	PUNCT
stem-4332	13	22	4	4	NUM
stem-4332	13	23	,	,	PUNCT
stem-4332	13	24	6	6	NUM
stem-4332	13	25	,	,	PUNCT
stem-4332	13	26	8	8	NUM
stem-4332	13	27	,	,	PUNCT
stem-4332	13	28	and	and	CCONJ
stem-4332	13	29	12	12	NUM
stem-4332	13	30	.	.	PUNCT
stem-4332	14	1	if	if	SCONJ
stem-4332	14	2	we	we	PRON
stem-4332	14	3	add	add	VERB
stem-4332	14	4	those	those	PRON
stem-4332	14	5	up	up	ADP
stem-4332	14	6	,	,	PUNCT
stem-4332	14	7	we	we	PRON
stem-4332	14	8	only	only	ADV
stem-4332	14	9	get	get	VERB
stem-4332	14	10	36	36	NUM
stem-4332	14	11	.	.	PUNCT
stem-4332	15	1	so	so	ADV
stem-4332	15	2	24	24	NUM
stem-4332	15	3	is	be	AUX
stem-4332	15	4	not	not	PART
stem-4332	15	5	a	a	DET
stem-4332	15	6	perfect	perfect	ADJ
stem-4332	15	7	number	number	NOUN
stem-4332	15	8	.	.	PUNCT
stem-4332	16	1	now	now	ADV
stem-4332	16	2	we	we	PRON
stem-4332	16	3	repeat	repeat	VERB
stem-4332	16	4	this	this	PRON
stem-4332	16	5	for	for	ADP
stem-4332	16	6	all	all	DET
stem-4332	16	7	the	the	DET
stem-4332	16	8	other	other	ADJ
stem-4332	16	9	numbers	number	NOUN
stem-4332	16	10	from	from	ADP
stem-4332	16	11	1	1	NUM
stem-4332	16	12	to	to	PART
stem-4332	16	13	100	100	NUM
stem-4332	16	14	and	and	CCONJ
stem-4332	16	15	see	see	VERB
stem-4332	16	16	that	that	SCONJ
stem-4332	16	17	only	only	ADV
stem-4332	16	18	6	6	NUM
stem-4332	16	19	and	and	CCONJ
stem-4332	16	20	28	28	NUM
stem-4332	16	21	are	be	AUX
stem-4332	16	22	perfect	perfect	ADJ
stem-4332	16	23	.	.	PUNCT
stem-4332	17	1	go	go	VERB
stem-4332	17	2	up	up	ADV
stem-4332	17	3	to	to	ADP
stem-4332	17	4	10000	10000	NUM
stem-4332	17	5	and	and	CCONJ
stem-4332	17	6	we	we	PRON
stem-4332	17	7	find	find	VERB
stem-4332	17	8	the	the	DET
stem-4332	17	9	next	next	ADJ
stem-4332	17	10	two	two	NUM
stem-4332	17	11	perfect	perfect	ADJ
stem-4332	17	12	numbers	number	NOUN
stem-4332	17	13	496	496	NUM
stem-4332	17	14	and	and	CCONJ
stem-4332	17	15	8128	8128	NUM
stem-4332	17	16	.	.	PUNCT
stem-4332	18	1	these	these	PRON
stem-4332	18	2	were	be	AUX
stem-4332	18	3	the	the	DET
stem-4332	18	4	only	only	ADJ
stem-4332	18	5	perfect	perfect	ADJ
stem-4332	18	6	numbers	number	NOUN
stem-4332	18	7	known	know	VERB
stem-4332	18	8	by	by	ADP
stem-4332	18	9	the	the	DET
stem-4332	18	10	ancient	ancient	ADJ
stem-4332	18	11	greeks	greeks	PROPN
stem-4332	18	12	,	,	PUNCT
stem-4332	18	13	and	and	CCONJ
stem-4332	18	14	they	they	PRON
stem-4332	18	15	would	would	AUX
stem-4332	18	16	be	be	AUX
stem-4332	18	17	the	the	DET
stem-4332	18	18	only	only	ADJ
stem-4332	18	19	known	know	VERB
stem-4332	18	20	ones	one	NOUN
stem-4332	18	21	for	for	ADP
stem-4332	18	22	over	over	ADP
stem-4332	18	23	a	a	DET
stem-4332	18	24	thousand	thousand	NUM
stem-4332	18	25	years	year	NOUN
stem-4332	18	26	.	.	PUNCT
stem-4332	19	1	6	6	NUM
stem-4332	19	2	28	28	NUM
stem-4332	19	3	496	496	NUM
stem-4332	19	4	8128	8128	NUM
stem-4332	19	5	consider	consider	VERB
stem-4332	19	6	the	the	DET
stem-4332	19	7	general	general	ADJ
stem-4332	19	8	features	feature	NOUN
stem-4332	19	9	of	of	ADP
stem-4332	19	10	perfect	perfect	ADJ
stem-4332	19	11	numbers	number	NOUN
stem-4332	19	12	.	.	PUNCT
stem-4332	20	1	one	one	NUM
stem-4332	20	2	thing	thing	NOUN
stem-4332	20	3	to	to	PART
stem-4332	20	4	notice	notice	VERB
stem-4332	20	5	is	be	AUX
stem-4332	20	6	that	that	SCONJ
stem-4332	20	7	each	each	DET
stem-4332	20	8	next	next	ADJ
stem-4332	20	9	perfect	perfect	ADJ
stem-4332	20	10	number	number	NOUN
stem-4332	20	11	is	be	AUX
stem-4332	20	12	one	one	NUM
stem-4332	20	13	digit	digit	NOUN
stem-4332	20	14	longer	long	ADJ
stem-4332	20	15	than	than	ADP
stem-4332	20	16	the	the	DET
stem-4332	20	17	number	number	NOUN
stem-4332	20	18	that	that	PRON
stem-4332	20	19	came	come	VERB
stem-4332	20	20	before	before	ADP
stem-4332	20	21	it	it	PRON
stem-4332	20	22	.	.	PUNCT
stem-4332	21	1	another	another	DET
stem-4332	21	2	thing	thing	NOUN
stem-4332	21	3	they	they	PRON
stem-4332	21	4	share	share	VERB
stem-4332	21	5	is	be	AUX
stem-4332	21	6	that	that	SCONJ
stem-4332	21	7	the	the	DET
stem-4332	21	8	ending	end	VERB
stem-4332	21	9	digit	digit	NOUN
stem-4332	21	10	alternates	alternate	NOUN
stem-4332	21	11	between	between	ADP
stem-4332	21	12	6	6	NUM
stem-4332	21	13	and	and	CCONJ
stem-4332	21	14	8	8	NUM
stem-4332	21	15	,	,	PUNCT
stem-4332	21	16	which	which	PRON
stem-4332	21	17	also	also	ADV
stem-4332	21	18	means	mean	VERB
stem-4332	21	19	they	they	PRON
stem-4332	21	20	are	be	AUX
stem-4332	21	21	all	all	ADV
stem-4332	21	22	even	even	ADV
stem-4332	21	23	.	.	PUNCT
stem-4332	22	1	but	but	CCONJ
stem-4332	22	2	here	here	ADV
stem-4332	22	3	's	be	AUX
stem-4332	22	4	where	where	SCONJ
stem-4332	22	5	things	thing	NOUN
stem-4332	22	6	get	get	VERB
stem-4332	22	7	really	really	ADV
stem-4332	22	8	weird	weird	ADJ
stem-4332	22	9	.	.	PUNCT
stem-4332	23	1	we	we	PRON
stem-4332	23	2	can	can	AUX
stem-4332	23	3	write	write	VERB
stem-4332	23	4	6	6	NUM
stem-4332	23	5	as	as	ADP
stem-4332	23	6	the	the	DET
stem-4332	23	7	sum	sum	NOUN
stem-4332	23	8	of	of	ADP
stem-4332	23	9	1	1	NUM
stem-4332	23	10	plus	plus	CCONJ
stem-4332	23	11	2	2	NUM
stem-4332	23	12	plus	plus	CCONJ
stem-4332	23	13	3	3	NUM
stem-4332	23	14	and	and	CCONJ
stem-4332	23	15	28	28	NUM
stem-4332	23	16	as	as	ADP
stem-4332	23	17	the	the	DET
stem-4332	23	18	sum	sum	NOUN
stem-4332	23	19	of	of	ADP
stem-4332	23	20	one	one	NUM
stem-4332	23	21	,	,	PUNCT
stem-4332	23	22	plus	plus	CCONJ
stem-4332	23	23	2	2	NUM
stem-4332	23	24	,	,	PUNCT
stem-4332	23	25	plus	plus	CCONJ
stem-4332	23	26	3	3	NUM
stem-4332	23	27	,	,	PUNCT
stem-4332	23	28	plus	plus	CCONJ
stem-4332	23	29	4	4	NUM
stem-4332	23	30	plus	plus	CCONJ
stem-4332	23	31	5	5	NUM
stem-4332	23	32	plus	plus	CCONJ
stem-4332	23	33	6	6	NUM
stem-4332	23	34	plus	plus	CCONJ
stem-4332	23	35	7	7	NUM
stem-4332	23	36	,	,	PUNCT
stem-4332	23	37	and	and	CCONJ
stem-4332	23	38	so	so	ADV
stem-4332	23	39	on	on	ADV
stem-4332	23	40	for	for	ADP
stem-4332	23	41	the	the	DET
stem-4332	23	42	others	other	NOUN
stem-4332	23	43	as	as	ADV
stem-4332	23	44	well	well	ADV
stem-4332	23	45	,	,	PUNCT
stem-4332	23	46	they	they	PRON
stem-4332	23	47	're	be	AUX
stem-4332	23	48	all	all	PRON
stem-4332	23	49	just	just	ADV
stem-4332	23	50	the	the	DET
stem-4332	23	51	sum	sum	NOUN
stem-4332	23	52	of	of	ADP
stem-4332	23	53	consecutive	consecutive	ADJ
stem-4332	23	54	numbers	number	NOUN
stem-4332	23	55	.	.	PUNCT
stem-4332	24	1	6	6	NUM
stem-4332	24	2	=	=	SYM
stem-4332	24	3	1	1	NUM
stem-4332	24	4	+	+	NUM
stem-4332	24	5	2	2	NUM
stem-4332	24	6	+	+	NUM
stem-4332	24	7	3	3	NUM
stem-4332	24	8	,	,	PUNCT
stem-4332	24	9	28	28	NUM
stem-4332	24	10	=	=	SYM
stem-4332	24	11	1	1	NUM
stem-4332	24	12	+	+	NUM
stem-4332	24	13	2	2	NUM
stem-4332	24	14	+	+	NUM
stem-4332	24	15	3	3	NUM
stem-4332	24	16	+	+	SYM
stem-4332	24	17	4	4	NUM
stem-4332	24	18	+	+	SYM
stem-4332	24	19	5	5	NUM
stem-4332	24	20	+	+	CCONJ
stem-4332	24	21	6	6	NUM
stem-4332	24	22	+	+	SYM
stem-4332	24	23	7	7	NUM
stem-4332	24	24	,	,	PUNCT
stem-4332	24	25	496	496	NUM
stem-4332	24	26	=	=	SYM
stem-4332	24	27	1	1	NUM
stem-4332	24	28	+	+	NUM
stem-4332	24	29	2	2	NUM
stem-4332	24	30	+	+	NUM
stem-4332	24	31	3	3	NUM
stem-4332	24	32	+	+	SYM
stem-4332	24	33	4	4	NUM
stem-4332	24	34	+	+	SYM
stem-4332	24	35	5	5	NUM
stem-4332	24	36	+	+	SYM
stem-4332	24	37	⋯	⋯	VERB
stem-4332	24	38	+	+	CCONJ
stem-4332	24	39	30	30	NUM
stem-4332	24	40	+	+	NUM
stem-4332	24	41	31	31	NUM
stem-4332	24	42	,	,	PUNCT
stem-4332	24	43	8128	8128	NUM
stem-4332	24	44	=	=	SYM
stem-4332	24	45	1	1	NUM
stem-4332	24	46	+	+	NUM
stem-4332	24	47	2	2	NUM
stem-4332	24	48	+	+	NUM
stem-4332	24	49	3	3	NUM
stem-4332	24	50	+	+	SYM
stem-4332	24	51	4	4	NUM
stem-4332	24	52	+	+	SYM
stem-4332	24	53	5	5	NUM
stem-4332	24	54	+	+	SYM
stem-4332	24	55	6	6	NUM
stem-4332	24	56	+	+	SYM
stem-4332	24	57	7	7	NUM
stem-4332	24	58	+	+	SYM
stem-4332	24	59	⋯	⋯	VERB
stem-4332	24	60	+	+	CCONJ
stem-4332	24	61	126	126	NUM
stem-4332	24	62	+	+	CCONJ
stem-4332	24	63	127	127	NUM
stem-4332	24	64	;	;	PUNCT
stem-4332	24	65	291	291	NUM
stem-4332	24	66	journal	journal	NOUN
stem-4332	24	67	of	of	ADP
stem-4332	24	68	language	language	NOUN
stem-4332	24	69	,	,	PUNCT
stem-4332	24	70	literacy	literacy	NOUN
stem-4332	24	71	and	and	CCONJ
stem-4332	24	72	learning	learn	VERB
stem-4332	24	73	in	in	ADP
stem-4332	24	74	stem	stem	NOUN
stem-4332	24	75	education	education	NOUN
stem-4332	24	76	www	www	PROPN
stem-4332	24	77	.	.	PUNCT
stem-4332	24	78	grnjournal.us	grnjournal.us	X
stem-4332	25	1	and	and	CCONJ
stem-4332	25	2	so	so	ADV
stem-4332	25	3	these	these	PRON
stem-4332	25	4	create	create	VERB
stem-4332	25	5	a	a	DET
stem-4332	25	6	triangle	triangle	NOUN
stem-4332	25	7	,	,	PUNCT
stem-4332	25	8	which	which	PRON
stem-4332	25	9	is	be	AUX
stem-4332	25	10	why	why	SCONJ
stem-4332	25	11	these	these	DET
stem-4332	25	12	numbers	number	NOUN
stem-4332	25	13	are	be	AUX
stem-4332	25	14	called	call	VERB
stem-4332	25	15	triangular	triangular	NOUN
stem-4332	25	16	numbers	number	NOUN
stem-4332	25	17	.	.	PUNCT
stem-4332	26	1	also	also	ADV
stem-4332	26	2	,	,	PUNCT
stem-4332	26	3	every	every	DET
stem-4332	26	4	number	number	NOUN
stem-4332	26	5	except	except	SCONJ
stem-4332	26	6	for	for	ADP
stem-4332	26	7	six	six	NUM
stem-4332	26	8	is	be	AUX
stem-4332	26	9	the	the	DET
stem-4332	26	10	sum	sum	NOUN
stem-4332	26	11	of	of	ADP
stem-4332	26	12	consecutive	consecutive	ADJ
stem-4332	26	13	odd	odd	ADJ
stem-4332	26	14	cubes	cube	NOUN
stem-4332	26	15	.	.	PUNCT
stem-4332	27	1	28	28	NUM
stem-4332	27	2	is	be	AUX
stem-4332	27	3	1	1	NUM
stem-4332	27	4	cubed	cubed	ADJ
stem-4332	27	5	plus	plus	CCONJ
stem-4332	27	6	3	3	NUM
stem-4332	27	7	cubed	cube	VERB
stem-4332	27	8	.	.	PUNCT
stem-4332	28	1	496	496	NUM
stem-4332	28	2	is	be	AUX
stem-4332	28	3	equal	equal	ADJ
stem-4332	28	4	to	to	ADP
stem-4332	28	5	1	1	NUM
stem-4332	28	6	cubed	cube	VERB
stem-4332	28	7	plus	plus	CCONJ
stem-4332	28	8	3	3	NUM
stem-4332	28	9	cubed	cube	VERB
stem-4332	28	10	plus	plus	CCONJ
stem-4332	28	11	5	5	NUM
stem-4332	28	12	cubed	cube	VERB
stem-4332	28	13	plus	plus	CCONJ
stem-4332	28	14	7	7	NUM
stem-4332	28	15	cubed	cube	VERB
stem-4332	28	16	.	.	PUNCT
stem-4332	29	1	and	and	CCONJ
stem-4332	29	2	8128	8128	NUM
stem-4332	29	3	is	be	AUX
stem-4332	29	4	equal	equal	ADJ
stem-4332	29	5	to	to	ADP
stem-4332	29	6	1	1	NUM
stem-4332	29	7	cubed	cube	VERB
stem-4332	29	8	plus	plus	CCONJ
stem-4332	29	9	3	3	NUM
stem-4332	29	10	cubed	cube	VERB
stem-4332	29	11	plus	plus	CCONJ
stem-4332	29	12	5	5	NUM
stem-4332	29	13	cubed	cube	VERB
stem-4332	29	14	plus	plus	CCONJ
stem-4332	29	15	7	7	NUM
stem-4332	29	16	cubed	cube	VERB
stem-4332	29	17	plus	plus	CCONJ
stem-4332	29	18	9	9	NUM
stem-4332	29	19	cubed	cube	VERB
stem-4332	29	20	all	all	DET
stem-4332	29	21	the	the	DET
stem-4332	29	22	way	way	NOUN
stem-4332	29	23	up	up	ADP
stem-4332	29	24	to	to	PART
stem-4332	29	25	15	15	NUM
stem-4332	29	26	cubed	cube	VERB
stem-4332	29	27	.	.	PUNCT
stem-4332	30	1	28	28	NUM
stem-4332	30	2	=	=	SYM
stem-4332	30	3	13	13	NUM
stem-4332	30	4	+	+	NUM
stem-4332	30	5	33	33	NUM
stem-4332	30	6	,	,	PUNCT
stem-4332	30	7	496	496	NUM
stem-4332	30	8	=	=	SYM
stem-4332	30	9	13	13	NUM
stem-4332	31	1	+	+	NUM
stem-4332	31	2	33	33	NUM
stem-4332	31	3	+	+	SYM
stem-4332	31	4	53	53	NUM
stem-4332	31	5	+	+	NUM
stem-4332	31	6	73	73	NUM
stem-4332	31	7	,	,	PUNCT
stem-4332	31	8	8128	8128	NUM
stem-4332	31	9	=	=	SYM
stem-4332	31	10	13	13	NUM
stem-4332	31	11	+	+	NUM
stem-4332	31	12	33	33	NUM
stem-4332	31	13	+	+	SYM
stem-4332	31	14	53	53	NUM
stem-4332	31	15	+	+	NUM
stem-4332	31	16	73	73	NUM
stem-4332	31	17	+	+	CCONJ
stem-4332	31	18	93	93	NUM
stem-4332	31	19	+	+	CCONJ
stem-4332	31	20	⋯	⋯	VERB
stem-4332	31	21	+	+	NOUN
stem-4332	31	22	153	153	NUM
stem-4332	31	23	;	;	PUNCT
stem-4332	31	24	if	if	SCONJ
stem-4332	31	25	we	we	PRON
stem-4332	31	26	write	write	VERB
stem-4332	31	27	these	these	DET
stem-4332	31	28	numbers	number	NOUN
stem-4332	31	29	in	in	ADP
stem-4332	31	30	binary	binary	ADJ
stem-4332	31	31	,	,	PUNCT
stem-4332	31	32	6	6	NUM
stem-4332	31	33	becomes	become	VERB
stem-4332	31	34	110	110	NUM
stem-4332	31	35	,	,	PUNCT
stem-4332	31	36	and	and	CCONJ
stem-4332	31	37	28	28	NUM
stem-4332	31	38	becomes	become	VERB
stem-4332	31	39	11100	11100	NUM
stem-4332	31	40	.	.	PUNCT
stem-4332	32	1	496	496	NUM
stem-4332	32	2	becomes	become	VERB
stem-4332	32	3	111110000	111110000	NUM
stem-4332	32	4	.	.	PUNCT
stem-4332	33	1	and	and	CCONJ
stem-4332	33	2	8128	8128	NUM
stem-4332	33	3	becomes	become	VERB
stem-4332	33	4	1111111000000	1111111000000	NUM
stem-4332	33	5	.	.	PUNCT
stem-4332	34	1	it	it	PRON
stem-4332	34	2	is	be	AUX
stem-4332	34	3	also	also	ADV
stem-4332	34	4	a	a	DET
stem-4332	34	5	string	string	NOUN
stem-4332	34	6	of	of	ADP
stem-4332	34	7	ones	one	NOUN
stem-4332	34	8	followed	follow	VERB
stem-4332	34	9	by	by	ADP
stem-4332	34	10	a	a	DET
stem-4332	34	11	series	series	NOUN
stem-4332	34	12	of	of	ADP
stem-4332	34	13	zeros	zero	NOUN
stem-4332	34	14	.	.	PUNCT
stem-4332	35	1	610	610	NUM
stem-4332	35	2	=	=	SYM
stem-4332	35	3	1102	1102	NUM
stem-4332	35	4	,	,	PUNCT
stem-4332	35	5	2810	2810	NUM
stem-4332	35	6	=	=	SYM
stem-4332	35	7	111002	111002	NUM
stem-4332	35	8	,	,	PUNCT
stem-4332	35	9	49610	49610	NUM
stem-4332	35	10	=	=	SYM
stem-4332	35	11	1111100002	1111100002	NUM
stem-4332	35	12	,	,	PUNCT
stem-4332	35	13	812810	812810	NUM
stem-4332	35	14	=	=	SYM
stem-4332	35	15	11111110000002	11111110000002	NUM
stem-4332	35	16	;	;	PUNCT
stem-4332	35	17	and	and	CCONJ
stem-4332	35	18	we	we	PRON
stem-4332	35	19	can	can	AUX
stem-4332	35	20	also	also	ADV
stem-4332	35	21	write	write	VERB
stem-4332	35	22	them	they	PRON
stem-4332	35	23	out	out	ADP
stem-4332	35	24	so	so	SCONJ
stem-4332	35	25	that	that	SCONJ
stem-4332	35	26	they	they	PRON
stem-4332	35	27	are	be	AUX
stem-4332	35	28	all	all	ADV
stem-4332	35	29	just	just	ADV
stem-4332	35	30	consecutive	consecutive	ADJ
stem-4332	35	31	powers	power	NOUN
stem-4332	35	32	of	of	ADP
stem-4332	35	33	two	two	NUM
stem-4332	35	34	.	.	PUNCT
stem-4332	36	1	6	6	NUM
stem-4332	36	2	=	=	SYM
stem-4332	36	3	22	22	NUM
stem-4332	36	4	+	+	NUM
stem-4332	36	5	21	21	NUM
stem-4332	36	6	,	,	PUNCT
stem-4332	36	7	28	28	NUM
stem-4332	36	8	=	=	SYM
stem-4332	36	9	24	24	NUM
stem-4332	36	10	+	+	NUM
stem-4332	36	11	23	23	NUM
stem-4332	37	1	+	+	NUM
stem-4332	37	2	22	22	NUM
stem-4332	37	3	,	,	PUNCT
stem-4332	37	4	496	496	NUM
stem-4332	38	1	=	=	SYM
stem-4332	38	2	28	28	NUM
stem-4332	38	3	+	+	NUM
stem-4332	38	4	27	27	NUM
stem-4332	38	5	+	+	NUM
stem-4332	38	6	26	26	NUM
stem-4332	38	7	+	+	CCONJ
stem-4332	38	8	25	25	NUM
stem-4332	38	9	+	+	NUM
stem-4332	38	10	24	24	NUM
stem-4332	38	11	,	,	PUNCT
stem-4332	38	12	8128	8128	NUM
stem-4332	38	13	=	=	SYM
stem-4332	39	1	212	212	NUM
stem-4332	39	2	+	+	NUM
stem-4332	39	3	211	211	NUM
stem-4332	39	4	+	+	NUM
stem-4332	39	5	210	210	NUM
stem-4332	39	6	+	+	CCONJ
stem-4332	39	7	29	29	NUM
stem-4332	39	8	+	+	NUM
stem-4332	39	9	28	28	NUM
stem-4332	39	10	+	+	NUM
stem-4332	39	11	27	27	NUM
stem-4332	39	12	+	+	CCONJ
stem-4332	39	13	26	26	NUM
stem-4332	39	14	;	;	PUNCT
stem-4332	39	15	so	so	ADV
stem-4332	39	16	a	a	DET
stem-4332	39	17	perfect	perfect	ADJ
stem-4332	39	18	number	number	NOUN
stem-4332	39	19	(	(	PUNCT
stem-4332	39	20	greek	greek	NOUN
stem-4332	39	21	:	:	PUNCT
stem-4332	39	22	ἀριθμὸς	ἀριθμὸς	PROPN
stem-4332	39	23	τέλειος	τέλειος	NOUN
stem-4332	39	24	)	)	PUNCT
stem-4332	39	25	is	be	AUX
stem-4332	39	26	a	a	DET
stem-4332	39	27	positive	positive	ADJ
stem-4332	39	28	integer	integer	NOUN
stem-4332	39	29	that	that	PRON
stem-4332	39	30	is	be	AUX
stem-4332	39	31	equal	equal	ADJ
stem-4332	39	32	to	to	ADP
stem-4332	39	33	the	the	DET
stem-4332	39	34	sum	sum	NOUN
stem-4332	39	35	of	of	ADP
stem-4332	39	36	all	all	PRON
stem-4332	39	37	its	its	PRON
stem-4332	39	38	own	own	ADJ
stem-4332	39	39	divisors	divisor	NOUN
stem-4332	39	40	(	(	PUNCT
stem-4332	39	41	that	that	PRON
stem-4332	39	42	is	is	ADV
stem-4332	39	43	,	,	PUNCT
stem-4332	39	44	all	all	DET
stem-4332	39	45	positive	positive	ADJ
stem-4332	39	46	divisors	divisor	NOUN
stem-4332	39	47	other	other	ADJ
stem-4332	39	48	than	than	ADP
stem-4332	39	49	the	the	DET
stem-4332	39	50	number	number	NOUN
stem-4332	39	51	itself	itself	PRON
stem-4332	39	52	)	)	PUNCT
stem-4332	39	53	.	.	PUNCT
stem-4332	40	1	the	the	DET
stem-4332	40	2	history	history	NOUN
stem-4332	40	3	what	what	PRON
stem-4332	40	4	now	now	ADV
stem-4332	40	5	around	around	ADP
stem-4332	40	6	300	300	NUM
stem-4332	40	7	bc	bc	PROPN
stem-4332	40	8	euclid	euclid	PROPN
stem-4332	40	9	discovered	discover	VERB
stem-4332	40	10	the	the	DET
stem-4332	40	11	pattern	pattern	NOUN
stem-4332	40	12	that	that	PRON
stem-4332	40	13	makes	make	VERB
stem-4332	40	14	these	these	DET
stem-4332	40	15	perfect	perfect	ADJ
stem-4332	40	16	numbers	number	NOUN
stem-4332	40	17	.	.	PUNCT
stem-4332	41	1	he	he	PRON
stem-4332	41	2	took	take	VERB
stem-4332	41	3	the	the	DET
stem-4332	41	4	number	number	NOUN
stem-4332	41	5	one	one	NUM
stem-4332	41	6	and	and	CCONJ
stem-4332	41	7	double	double	ADJ
stem-4332	41	8	it	it	PRON
stem-4332	41	9	,	,	PUNCT
stem-4332	41	10	he	he	PRON
stem-4332	41	11	got	get	VERB
stem-4332	41	12	two	two	NUM
stem-4332	41	13	,	,	PUNCT
stem-4332	41	14	keep	keep	VERB
stem-4332	41	15	doubled	double	VERB
stem-4332	41	16	it	it	PRON
stem-4332	41	17	and	and	CCONJ
stem-4332	41	18	get	get	VERB
stem-4332	41	19	4	4	NUM
stem-4332	41	20	,	,	PUNCT
stem-4332	41	21	8	8	NUM
stem-4332	41	22	,	,	PUNCT
stem-4332	41	23	16	16	NUM
stem-4332	41	24	,	,	PUNCT
stem-4332	41	25	32	32	NUM
stem-4332	41	26	,	,	PUNCT
stem-4332	41	27	64	64	NUM
stem-4332	41	28	,	,	PUNCT
stem-4332	41	29	and	and	CCONJ
stem-4332	41	30	so	so	ADV
stem-4332	41	31	on	on	ADV
stem-4332	41	32	.	.	PROPN
stem-4332	42	1	1	1	NUM
stem-4332	42	2	,	,	PUNCT
stem-4332	42	3	2	2	NUM
stem-4332	42	4	,	,	PUNCT
stem-4332	42	5	4	4	NUM
stem-4332	42	6	,	,	PUNCT
stem-4332	42	7	8	8	NUM
stem-4332	42	8	,	,	PUNCT
stem-4332	42	9	16	16	NUM
stem-4332	42	10	,	,	PUNCT
stem-4332	42	11	32	32	NUM
stem-4332	42	12	,	,	PUNCT
stem-4332	42	13	64	64	NUM
stem-4332	42	14	,	,	PUNCT
stem-4332	42	15	128	128	NUM
stem-4332	42	16	,	,	PUNCT
stem-4332	42	17	⋯	⋯	VERB
stem-4332	42	18	he	he	PRON
stem-4332	42	19	started	start	VERB
stem-4332	42	20	from	from	ADP
stem-4332	42	21	one	one	NUM
stem-4332	42	22	and	and	CCONJ
stem-4332	42	23	added	add	VERB
stem-4332	42	24	the	the	DET
stem-4332	42	25	next	next	ADJ
stem-4332	42	26	number	number	NOUN
stem-4332	42	27	to	to	ADP
stem-4332	42	28	it	it	PRON
stem-4332	42	29	.	.	PUNCT
stem-4332	43	1	if	if	SCONJ
stem-4332	43	2	that	that	PRON
stem-4332	43	3	added	add	VERB
stem-4332	43	4	up	up	ADP
stem-4332	43	5	to	to	ADP
stem-4332	43	6	a	a	DET
stem-4332	43	7	prime	prime	NOUN
stem-4332	43	8	,	,	PUNCT
stem-4332	43	9	then	then	ADV
stem-4332	43	10	he	he	PRON
stem-4332	43	11	multiplied	multiply	VERB
stem-4332	43	12	it	it	PRON
stem-4332	43	13	by	by	ADP
stem-4332	43	14	the	the	DET
stem-4332	43	15	last	last	ADJ
stem-4332	43	16	number	number	NOUN
stem-4332	43	17	in	in	ADP
stem-4332	43	18	the	the	DET
stem-4332	43	19	sequence	sequence	NOUN
stem-4332	43	20	to	to	PART
stem-4332	43	21	get	get	VERB
stem-4332	43	22	a	a	DET
stem-4332	43	23	perfect	perfect	ADJ
stem-4332	43	24	number	number	NOUN
stem-4332	43	25	.	.	PUNCT
stem-4332	44	1	that	that	PRON
stem-4332	44	2	is	be	AUX
stem-4332	44	3	:	:	PUNCT
stem-4332	44	4	1	1	NUM
stem-4332	44	5	+	+	SYM
stem-4332	44	6	2	2	NUM
stem-4332	44	7	=	=	SYM
stem-4332	44	8	3	3	NUM
stem-4332	44	9	,	,	PUNCT
stem-4332	44	10	2	2	NUM
stem-4332	44	11	∙	∙	PROPN
stem-4332	44	12	3	3	NUM
stem-4332	44	13	=	=	SYM
stem-4332	44	14	6	6	NUM
stem-4332	45	1	thus	thus	ADV
stem-4332	45	2	two	two	NUM
stem-4332	45	3	times	time	NOUN
stem-4332	45	4	three	three	NUM
stem-4332	45	5	equals	equal	VERB
stem-4332	45	6	six	six	NUM
stem-4332	45	7	,	,	PUNCT
stem-4332	45	8	the	the	DET
stem-4332	45	9	first	first	ADJ
stem-4332	45	10	perfect	perfect	ADJ
stem-4332	45	11	number	number	NOUN
stem-4332	45	12	.	.	PUNCT
stem-4332	46	1	and	and	CCONJ
stem-4332	46	2	so	so	ADV
stem-4332	46	3	euclid	euclid	PROPN
stem-4332	46	4	found	find	VERB
stem-4332	46	5	a	a	DET
stem-4332	46	6	way	way	NOUN
stem-4332	46	7	to	to	PART
stem-4332	46	8	generate	generate	VERB
stem-4332	46	9	even	even	ADV
stem-4332	46	10	perfect	perfect	ADJ
stem-4332	46	11	numbers	number	NOUN
stem-4332	46	12	,	,	PUNCT
stem-4332	46	13	but	but	CCONJ
stem-4332	46	14	he	he	PRON
stem-4332	46	15	did	do	AUX
stem-4332	46	16	n't	not	PART
stem-4332	46	17	prove	prove	VERB
stem-4332	46	18	that	that	SCONJ
stem-4332	46	19	this	this	PRON
stem-4332	46	20	was	be	AUX
stem-4332	46	21	the	the	DET
stem-4332	46	22	only	only	ADJ
stem-4332	46	23	way	way	NOUN
stem-4332	46	24	.	.	PUNCT
stem-4332	47	1	and	and	CCONJ
stem-4332	47	2	formula	formula	NOUN
stem-4332	47	3	that	that	PRON
stem-4332	47	4	gives	give	VERB
stem-4332	47	5	a	a	DET
stem-4332	47	6	perfect	perfect	ADJ
stem-4332	47	7	number	number	NOUN
stem-4332	47	8	is	be	AUX
stem-4332	47	9	(	(	PUNCT
stem-4332	47	10	𝟐𝒑	𝟐𝒑	NOUN
stem-4332	47	11	−	−	PROPN
stem-4332	47	12	𝟏	𝟏	NUM
stem-4332	47	13	)	)	PUNCT
stem-4332	47	14	∙	∙	NOUN
stem-4332	47	15	𝟐𝒑	𝟐𝒑	NOUN
stem-4332	47	16	.	.	PUNCT
stem-4332	48	1	400	400	NUM
stem-4332	48	2	years	year	NOUN
stem-4332	48	3	later	later	ADV
stem-4332	48	4	,	,	PUNCT
stem-4332	48	5	the	the	DET
stem-4332	48	6	greek	greek	ADJ
stem-4332	48	7	philosopher	philosopher	NOUN
stem-4332	48	8	nicomachus	nicomachus	NOUN
stem-4332	48	9	published	publish	VERB
stem-4332	48	10	«	«	PUNCT
stem-4332	48	11	introdutio	introdutio	PROPN
stem-4332	48	12	arithmetica	arithmetica	PROPN
stem-4332	48	13	»	»	PROPN
stem-4332	48	14	,	,	PUNCT
stem-4332	48	15	the	the	DET
stem-4332	48	16	standard	standard	ADJ
stem-4332	48	17	arithmetic	arithmetic	ADJ
stem-4332	48	18	textfor	textfor	NOUN
stem-4332	48	19	the	the	DET
stem-4332	48	20	next	next	ADJ
stem-4332	48	21	thousand	thousand	NUM
stem-4332	48	22	years	year	NOUN
stem-4332	48	23	.	.	PUNCT
stem-4332	49	1	in	in	ADP
stem-4332	49	2	it	it	PRON
stem-4332	49	3	,	,	PUNCT
stem-4332	49	4	he	he	PRON
stem-4332	49	5	stated	state	VERB
stem-4332	49	6	five	five	NUM
stem-4332	49	7	conjectures	conjecture	VERB
stem-4332	49	8	statements	statement	NOUN
stem-4332	49	9	he	he	PRON
stem-4332	49	10	believed	believe	VERB
stem-4332	49	11	to	to	PART
stem-4332	49	12	be	be	AUX
stem-4332	49	13	true	true	ADJ
stem-4332	49	14	,	,	PUNCT
stem-4332	49	15	but	but	CCONJ
stem-4332	49	16	did	do	AUX
stem-4332	49	17	not	not	PART
stem-4332	49	18	bother	bother	VERB
stem-4332	49	19	actually	actually	ADV
stem-4332	49	20	trying	try	VERB
stem-4332	49	21	to	to	PART
stem-4332	49	22	prove	prove	VERB
stem-4332	49	23	.	.	PUNCT
stem-4332	50	1	his	his	PRON
stem-4332	50	2	conjectures	conjecture	NOUN
stem-4332	50	3	were	be	AUX
stem-4332	50	4	:	:	PUNCT
stem-4332	50	5	1	1	X
stem-4332	50	6	.	.	X
stem-4332	51	1	the	the	DET
stem-4332	51	2	nth	nth	NOUN
stem-4332	51	3	perfect	perfect	ADJ
stem-4332	51	4	number	number	NOUN
stem-4332	51	5	has	have	VERB
stem-4332	51	6	n	n	NUM
stem-4332	51	7	digits	digit	NOUN
stem-4332	51	8	.	.	PUNCT
stem-4332	52	1	2	2	X
stem-4332	52	2	.	.	X
stem-4332	52	3	all	all	DET
stem-4332	52	4	perfect	perfect	ADJ
stem-4332	52	5	numbers	number	NOUN
stem-4332	52	6	are	be	AUX
stem-4332	52	7	even	even	ADV
stem-4332	52	8	.	.	PUNCT
stem-4332	53	1	3	3	X
stem-4332	53	2	.	.	X
stem-4332	53	3	all	all	DET
stem-4332	53	4	perfect	perfect	ADJ
stem-4332	53	5	numbers	number	NOUN
stem-4332	53	6	end	end	VERB
stem-4332	53	7	in	in	ADP
stem-4332	53	8	6	6	NUM
stem-4332	53	9	and	and	CCONJ
stem-4332	53	10	8	8	NUM
stem-4332	53	11	alternately	alternately	ADV
stem-4332	53	12	.	.	PUNCT
stem-4332	54	1	4	4	X
stem-4332	54	2	.	.	X
stem-4332	54	3	euclid	euclid	PROPN
stem-4332	54	4	algorithm	algorithm	PROPN
stem-4332	54	5	produces	produce	VERB
stem-4332	54	6	every	every	DET
stem-4332	54	7	even	even	ADV
stem-4332	54	8	perfect	perfect	ADJ
stem-4332	54	9	number	number	NOUN
stem-4332	54	10	.	.	PUNCT
stem-4332	55	1	5	5	X
stem-4332	55	2	.	.	X
stem-4332	55	3	there	there	PRON
stem-4332	55	4	are	be	VERB
stem-4332	55	5	infinitely	infinitely	ADV
stem-4332	55	6	many	many	ADJ
stem-4332	55	7	perfect	perfect	ADJ
stem-4332	55	8	numbers	number	NOUN
stem-4332	55	9	.	.	PUNCT
stem-4332	56	1	292	292	NUM
stem-4332	56	2	journal	journal	NOUN
stem-4332	56	3	of	of	ADP
stem-4332	56	4	language	language	NOUN
stem-4332	56	5	,	,	PUNCT
stem-4332	56	6	literacy	literacy	NOUN
stem-4332	56	7	and	and	CCONJ
stem-4332	56	8	learning	learn	VERB
stem-4332	56	9	in	in	ADP
stem-4332	56	10	stem	stem	NOUN
stem-4332	56	11	education	education	NOUN
stem-4332	56	12	www	www	PROPN
stem-4332	56	13	.	.	PUNCT
stem-4332	57	1	grnjournal.us	grnjournal.us	X
stem-4332	57	2	for	for	ADP
stem-4332	57	3	the	the	DET
stem-4332	57	4	next	next	ADJ
stem-4332	57	5	thousand	thousand	NUM
stem-4332	57	6	years	year	NOUN
stem-4332	57	7	no	no	DET
stem-4332	57	8	one	one	PRON
stem-4332	57	9	could	could	AUX
stem-4332	57	10	prove	prove	VERB
stem-4332	57	11	or	or	CCONJ
stem-4332	57	12	disprove	disprove	VERB
stem-4332	57	13	any	any	PRON
stem-4332	57	14	of	of	ADP
stem-4332	57	15	these	these	DET
stem-4332	57	16	conjectures	conjecture	NOUN
stem-4332	57	17	,	,	PUNCT
stem-4332	57	18	and	and	CCONJ
stem-4332	57	19	they	they	PRON
stem-4332	57	20	were	be	AUX
stem-4332	57	21	considered	consider	VERB
stem-4332	57	22	facts	fact	NOUN
stem-4332	57	23	.	.	PUNCT
stem-4332	58	1	but	but	CCONJ
stem-4332	58	2	in	in	ADP
stem-4332	58	3	the	the	DET
stem-4332	58	4	13th	13th	ADJ
stem-4332	58	5	century	century	NOUN
stem-4332	58	6	,	,	PUNCT
stem-4332	58	7	egyptian	egyptian	ADJ
stem-4332	58	8	mathematician	mathematician	NOUN
stem-4332	58	9	ibn	ibn	PROPN
stem-4332	58	10	fallus	fallus	NOUN
stem-4332	58	11	published	publish	VERB
stem-4332	58	12	a	a	DET
stem-4332	58	13	list	list	NOUN
stem-4332	58	14	with	with	ADP
stem-4332	58	15	10	10	NUM
stem-4332	58	16	perfect	perfect	ADJ
stem-4332	58	17	numbers	number	NOUN
stem-4332	58	18	and	and	CCONJ
stem-4332	58	19	their	their	PRON
stem-4332	58	20	values	value	NOUN
stem-4332	58	21	of	of	ADP
stem-4332	58	22	p.	p.	NOUN
stem-4332	58	23	three	three	NUM
stem-4332	58	24	of	of	ADP
stem-4332	58	25	these	these	DET
stem-4332	58	26	perfect	perfect	ADJ
stem-4332	58	27	numbers	number	NOUN
stem-4332	58	28	turned	turn	VERB
stem-4332	58	29	out	out	ADP
stem-4332	58	30	not	not	PART
stem-4332	58	31	to	to	PART
stem-4332	58	32	be	be	AUX
stem-4332	58	33	perfect	perfect	ADJ
stem-4332	58	34	at	at	ADV
stem-4332	58	35	all	all	ADV
stem-4332	58	36	.	.	PUNCT
stem-4332	59	1	p	p	X
stem-4332	59	2	perfect	perfect	ADJ
stem-4332	59	3	number	number	NOUN
stem-4332	59	4	(	(	PUNCT
stem-4332	59	5	2𝑝	2𝑝	NOUN
stem-4332	59	6	−	−	NOUN
stem-4332	59	7	1	1	NUM
stem-4332	59	8	)	)	PUNCT
stem-4332	59	9	∙	∙	PROPN
stem-4332	59	10	2𝑝	2𝑝	NOUN
stem-4332	59	11	2	2	NUM
stem-4332	59	12	3	3	NUM
stem-4332	59	13	5	5	NUM
stem-4332	59	14	7	7	NUM
stem-4332	59	15	9	9	NUM
stem-4332	59	16	11	11	NUM
stem-4332	59	17	13	13	NUM
stem-4332	59	18	17	17	NUM
stem-4332	59	19	19	19	NUM
stem-4332	59	20	23	23	NUM
stem-4332	59	21	6	6	NUM
stem-4332	59	22	28	28	NUM
stem-4332	59	23	496	496	NUM
stem-4332	59	24	8	8	NUM
stem-4332	59	25	128	128	NUM
stem-4332	59	26	130	130	NUM
stem-4332	59	27	816	816	NUM
stem-4332	59	28	2	2	NUM
stem-4332	59	29	096	096	NUM
stem-4332	59	30	128	128	NUM
stem-4332	59	31	33	33	NUM
stem-4332	59	32	550	550	NUM
stem-4332	59	33	336	336	NUM
stem-4332	59	34	8	8	NUM
stem-4332	59	35	589	589	NUM
stem-4332	59	36	869	869	NUM
stem-4332	59	37	056	056	NUM
stem-4332	59	38	137	137	NUM
stem-4332	59	39	438	438	NUM
stem-4332	59	40	691	691	NUM
stem-4332	59	41	328	328	NUM
stem-4332	59	42	35	35	NUM
stem-4332	59	43	184	184	NUM
stem-4332	59	44	367	367	NUM
stem-4332	59	45	894	894	NUM
stem-4332	59	46	528	528	NUM
stem-4332	59	47	but	but	CCONJ
stem-4332	59	48	the	the	DET
stem-4332	59	49	remaining	remain	VERB
stem-4332	59	50	ones	one	NOUN
stem-4332	59	51	are	be	AUX
stem-4332	59	52	.	.	PUNCT
stem-4332	60	1	the	the	DET
stem-4332	60	2	fifth	fifth	ADJ
stem-4332	60	3	perfect	perfect	ADJ
stem-4332	60	4	number	number	NOUN
stem-4332	60	5	is	be	AUX
stem-4332	60	6	eight	eight	NUM
stem-4332	60	7	digits	digit	NOUN
stem-4332	60	8	long	long	ADV
stem-4332	60	9	,	,	PUNCT
stem-4332	60	10	which	which	PRON
stem-4332	60	11	disproves	disprove	VERB
stem-4332	60	12	nicomachus	nicomachus	NOUN
stem-4332	60	13	's	's	PART
stem-4332	60	14	first	first	ADJ
stem-4332	60	15	conjecture	conjecture	NOUN
stem-4332	60	16	.	.	PUNCT
stem-4332	61	1	and	and	CCONJ
stem-4332	61	2	the	the	DET
stem-4332	61	3	next	next	ADJ
stem-4332	61	4	thing	thing	NOUN
stem-4332	61	5	to	to	PART
stem-4332	61	6	notice	notice	VERB
stem-4332	61	7	is	be	AUX
stem-4332	61	8	that	that	SCONJ
stem-4332	61	9	both	both	CCONJ
stem-4332	61	10	the	the	DET
stem-4332	61	11	fifth	fifth	ADJ
stem-4332	61	12	and	and	CCONJ
stem-4332	61	13	sixth	sixth	ADJ
stem-4332	61	14	perfect	perfect	ADJ
stem-4332	61	15	number	number	NOUN
stem-4332	61	16	end	end	NOUN
stem-4332	61	17	in	in	ADP
stem-4332	61	18	a	a	DET
stem-4332	61	19	6	6	NUM
stem-4332	61	20	.	.	PUNCT
stem-4332	62	1	so	so	SCONJ
stem-4332	62	2	that	that	SCONJ
stem-4332	62	3	disproves	disprove	VERB
stem-4332	62	4	nicomachus	nicomachus	NOUN
stem-4332	62	5	's	's	PART
stem-4332	62	6	third	third	ADJ
stem-4332	62	7	conjecture	conjecture	NOUN
stem-4332	62	8	that	that	SCONJ
stem-4332	62	9	all	all	DET
stem-4332	62	10	perfect	perfect	ADJ
stem-4332	62	11	numbers	number	NOUN
stem-4332	62	12	end	end	VERB
stem-4332	62	13	in	in	ADP
stem-4332	62	14	a	a	DET
stem-4332	62	15	6	6	NUM
stem-4332	62	16	or	or	CCONJ
stem-4332	62	17	8	8	NUM
stem-4332	62	18	alternately	alternately	ADV
stem-4332	62	19	.	.	PUNCT
stem-4332	63	1	two	two	NUM
stem-4332	63	2	conjectures	conjecture	NOUN
stem-4332	63	3	were	be	AUX
stem-4332	63	4	proven	prove	VERB
stem-4332	63	5	false	false	ADJ
stem-4332	63	6	.	.	PUNCT
stem-4332	64	1	two	two	NUM
stem-4332	64	2	centuries	century	NOUN
stem-4332	64	3	later	later	ADV
stem-4332	64	4	,	,	PUNCT
stem-4332	64	5	the	the	DET
stem-4332	64	6	problem	problem	NOUN
stem-4332	64	7	reached	reach	VERB
stem-4332	64	8	renaissance	renaissance	PROPN
stem-4332	64	9	europe	europe	PROPN
stem-4332	64	10	where	where	SCONJ
stem-4332	64	11	they	they	PRON
stem-4332	64	12	rediscovered	rediscover	VERB
stem-4332	64	13	the	the	DET
stem-4332	64	14	fifth	fifth	ADJ
stem-4332	64	15	,	,	PUNCT
stem-4332	64	16	sixth	sixth	ADJ
stem-4332	64	17	,	,	PUNCT
stem-4332	64	18	and	and	CCONJ
stem-4332	64	19	seventh	seventh	ADJ
stem-4332	64	20	perfect	perfect	ADJ
stem-4332	64	21	numbers	number	NOUN
stem-4332	64	22	.	.	PUNCT
stem-4332	65	1	so	so	ADV
stem-4332	65	2	far	far	ADV
stem-4332	65	3	every	every	DET
stem-4332	65	4	perfect	perfect	ADJ
stem-4332	65	5	number	number	NOUN
stem-4332	65	6	had	have	VERB
stem-4332	65	7	euclid	euclid	PROPN
stem-4332	65	8	's	's	PART
stem-4332	65	9	form	form	NOUN
stem-4332	65	10	.	.	PUNCT
stem-4332	66	1	and	and	CCONJ
stem-4332	66	2	the	the	DET
stem-4332	66	3	best	good	ADJ
stem-4332	66	4	way	way	NOUN
stem-4332	66	5	to	to	PART
stem-4332	66	6	find	find	VERB
stem-4332	66	7	new	new	ADJ
stem-4332	66	8	ones	one	NOUN
stem-4332	66	9	was	be	AUX
stem-4332	66	10	by	by	ADP
stem-4332	66	11	finding	find	VERB
stem-4332	66	12	the	the	DET
stem-4332	66	13	values	value	NOUN
stem-4332	66	14	of	of	ADP
stem-4332	66	15	p	p	NOUN
stem-4332	66	16	that	that	PRON
stem-4332	66	17	make	make	VERB
stem-4332	66	18	(	(	PUNCT
stem-4332	66	19	2𝑝	2𝑝	NOUN
stem-4332	66	20	−	−	NOUN
stem-4332	66	21	1	1	NUM
stem-4332	66	22	)	)	PUNCT
stem-4332	66	23	prime	prime	NOUN
stem-4332	66	24	.	.	PUNCT
stem-4332	67	1	so	so	ADV
stem-4332	67	2	french	french	ADJ
stem-4332	67	3	polymath	polymath	PROPN
stem-4332	67	4	marin	marin	PROPN
stem-4332	67	5	mersenne	mersenne	PROPN
stem-4332	67	6	extensively	extensively	ADV
stem-4332	67	7	studied	study	VERB
stem-4332	67	8	numbers	number	NOUN
stem-4332	67	9	of	of	ADP
stem-4332	67	10	this	this	DET
stem-4332	67	11	form	form	NOUN
stem-4332	67	12	.	.	PUNCT
stem-4332	68	1	in	in	ADP
stem-4332	68	2	1644	1644	NUM
stem-4332	68	3	,	,	PUNCT
stem-4332	68	4	he	he	PRON
stem-4332	68	5	published	publish	VERB
stem-4332	68	6	his	his	PRON
stem-4332	68	7	in	in	ADP
stem-4332	68	8	a	a	DET
stem-4332	68	9	book	book	NOUN
stem-4332	68	10	including	include	VERB
stem-4332	68	11	a	a	DET
stem-4332	68	12	list	list	NOUN
stem-4332	68	13	of	of	ADP
stem-4332	68	14	11	11	NUM
stem-4332	68	15	values	value	NOUN
stem-4332	68	16	of	of	ADP
stem-4332	68	17	p	p	NOUN
stem-4332	68	18	for	for	ADP
stem-4332	68	19	which	which	PRON
stem-4332	68	20	he	he	PRON
stem-4332	68	21	claimed	claim	VERB
stem-4332	68	22	they	they	PRON
stem-4332	68	23	corresponded	correspond	VERB
stem-4332	68	24	to	to	ADP
stem-4332	68	25	primes	prime	NOUN
stem-4332	68	26	.	.	PUNCT
stem-4332	69	1	numbers	number	NOUN
stem-4332	69	2	for	for	ADP
stem-4332	69	3	which	which	PRON
stem-4332	69	4	this	this	PRON
stem-4332	69	5	is	be	AUX
stem-4332	69	6	true	true	ADJ
stem-4332	69	7	are	be	AUX
stem-4332	69	8	now	now	ADV
stem-4332	69	9	called	call	VERB
stem-4332	69	10	mersenne	mersenne	NOUN
stem-4332	69	11	primes	prime	NOUN
stem-4332	69	12	.	.	PUNCT
stem-4332	70	1	of	of	ADP
stem-4332	70	2	his	his	PRON
stem-4332	70	3	list	list	NOUN
stem-4332	70	4	the	the	DET
stem-4332	70	5	first	first	ADJ
stem-4332	70	6	seven	seven	NUM
stem-4332	70	7	exponents	exponent	NOUN
stem-4332	70	8	of	of	ADP
stem-4332	70	9	p	p	NOUN
stem-4332	70	10	do	do	AUX
stem-4332	70	11	result	result	VERB
stem-4332	70	12	in	in	ADP
stem-4332	70	13	primes	prime	NOUN
stem-4332	70	14	and	and	CCONJ
stem-4332	70	15	they	they	PRON
stem-4332	70	16	correspond	correspond	VERB
stem-4332	70	17	to	to	ADP
stem-4332	70	18	the	the	DET
stem-4332	70	19	first	first	ADJ
stem-4332	70	20	seven	seven	NUM
stem-4332	70	21	perfect	perfect	ADJ
stem-4332	70	22	numbers	number	NOUN
stem-4332	70	23	.	.	PUNCT
stem-4332	71	1	but	but	CCONJ
stem-4332	71	2	for	for	ADP
stem-4332	71	3	some	some	PRON
stem-4332	71	4	of	of	ADP
stem-4332	71	5	the	the	DET
stem-4332	71	6	larger	large	ADJ
stem-4332	71	7	numbers	number	NOUN
stem-4332	71	8	like	like	ADP
stem-4332	71	9	267	267	NUM
stem-4332	71	10	−1	−1	NOUN
stem-4332	71	11	,	,	PUNCT
stem-4332	71	12	mersenne	mersenne	PROPN
stem-4332	71	13	admitted	admit	VERB
stem-4332	71	14	to	to	PART
stem-4332	71	15	not	not	PART
stem-4332	71	16	even	even	ADV
stem-4332	71	17	checking	check	VERB
stem-4332	71	18	whether	whether	SCONJ
stem-4332	71	19	they	they	PRON
stem-4332	71	20	were	be	AUX
stem-4332	71	21	prime	prime	ADJ
stem-4332	71	22	.	.	PUNCT
stem-4332	72	1	he	he	PRON
stem-4332	72	2	was	be	AUX
stem-4332	72	3	saying	say	VERB
stem-4332	72	4	:	:	PUNCT
stem-4332	72	5	"	"	PUNCT
stem-4332	72	6	to	to	PART
stem-4332	72	7	tell	tell	VERB
stem-4332	72	8	if	if	SCONJ
stem-4332	72	9	a	a	DET
stem-4332	72	10	given	give	VERB
stem-4332	72	11	number	number	NOUN
stem-4332	72	12	of	of	ADP
stem-4332	72	13	15	15	NUM
stem-4332	72	14	to	to	PART
stem-4332	72	15	20	20	NUM
stem-4332	72	16	digits	digit	NOUN
stem-4332	72	17	is	be	AUX
stem-4332	72	18	prime	prime	ADJ
stem-4332	72	19	or	or	CCONJ
stem-4332	72	20	not	not	PART
stem-4332	72	21	all	all	DET
stem-4332	72	22	time	time	NOUN
stem-4332	72	23	would	would	AUX
stem-4332	72	24	not	not	PART
stem-4332	72	25	suffice	suffice	VERB
stem-4332	72	26	for	for	ADP
stem-4332	72	27	the	the	DET
stem-4332	72	28	test	test	NOUN
stem-4332	72	29	"	"	PUNCT
stem-4332	72	30	.	.	PUNCT
stem-4332	73	1	mersenne	mersenne	PROPN
stem-4332	73	2	discussed	discuss	VERB
stem-4332	73	3	the	the	DET
stem-4332	73	4	problem	problem	NOUN
stem-4332	73	5	of	of	ADP
stem-4332	73	6	perfect	perfect	ADJ
stem-4332	73	7	numbers	number	NOUN
stem-4332	73	8	with	with	ADP
stem-4332	73	9	other	other	ADJ
stem-4332	73	10	mathematicians	mathematician	NOUN
stem-4332	73	11	of	of	ADP
stem-4332	73	12	the	the	DET
stem-4332	73	13	time	time	NOUN
stem-4332	73	14	,	,	PUNCT
stem-4332	73	15	including	include	VERB
stem-4332	73	16	pierre	pierre	PROPN
stem-4332	73	17	de	de	X
stem-4332	73	18	fermat	fermat	PROPN
stem-4332	73	19	and	and	CCONJ
stem-4332	73	20	rene	rene	PROPN
stem-4332	73	21	descartes	descarte	NOUN
stem-4332	73	22	.	.	PUNCT
stem-4332	74	1	in	in	ADP
stem-4332	74	2	1638	1638	NUM
stem-4332	74	3	,	,	PUNCT
stem-4332	74	4	descartes	descartes	PROPN
stem-4332	74	5	wrote	write	VERB
stem-4332	74	6	to	to	ADP
stem-4332	74	7	mersenne	mersenne	NOUN
stem-4332	74	8	,	,	PUNCT
stem-4332	74	9	"	"	PUNCT
stem-4332	74	10	i	i	PRON
stem-4332	74	11	think	think	VERB
stem-4332	74	12	i	i	PRON
stem-4332	74	13	can	can	AUX
stem-4332	74	14	show	show	VERB
stem-4332	74	15	that	that	SCONJ
stem-4332	74	16	there	there	PRON
stem-4332	74	17	are	be	VERB
stem-4332	74	18	no	no	DET
stem-4332	74	19	even	even	ADV
stem-4332	74	20	perfect	perfect	ADJ
stem-4332	74	21	numbers	number	NOUN
stem-4332	74	22	except	except	SCONJ
stem-4332	74	23	those	those	PRON
stem-4332	74	24	of	of	ADP
stem-4332	74	25	euclid	euclid	PROPN
stem-4332	74	26	"	"	PUNCT
stem-4332	74	27	.	.	PUNCT
stem-4332	75	1	he	he	PRON
stem-4332	75	2	also	also	ADV
stem-4332	75	3	believed	believe	VERB
stem-4332	75	4	that	that	SCONJ
stem-4332	75	5	if	if	SCONJ
stem-4332	75	6	an	an	DET
stem-4332	75	7	odd	odd	ADJ
stem-4332	75	8	perfect	perfect	ADJ
stem-4332	75	9	number	number	NOUN
stem-4332	75	10	does	do	AUX
stem-4332	75	11	exist	exist	VERB
stem-4332	75	12	,	,	PUNCT
stem-4332	75	13	it	it	PRON
stem-4332	75	14	must	must	AUX
stem-4332	75	15	have	have	VERB
stem-4332	75	16	a	a	DET
stem-4332	75	17	special	special	ADJ
stem-4332	75	18	form	form	NOUN
stem-4332	75	19	.	.	PUNCT
stem-4332	76	1	it	it	PRON
stem-4332	76	2	must	must	AUX
stem-4332	76	3	be	be	AUX
stem-4332	76	4	the	the	DET
stem-4332	76	5	product	product	NOUN
stem-4332	76	6	of	of	ADP
stem-4332	76	7	a	a	DET
stem-4332	76	8	prime	prime	NOUN
stem-4332	76	9	and	and	CCONJ
stem-4332	76	10	the	the	DET
stem-4332	76	11	square	square	NOUN
stem-4332	76	12	of	of	ADP
stem-4332	76	13	a	a	DET
stem-4332	76	14	different	different	ADJ
stem-4332	76	15	number	number	NOUN
stem-4332	76	16	,	,	PUNCT
stem-4332	76	17	that	that	PRON
stem-4332	76	18	is	be	AUX
stem-4332	76	19	𝑁	𝑁	PROPN
stem-4332	76	20	=	=	SYM
stem-4332	76	21	𝑝𝑠𝑀2	𝑝𝑠𝑀2	PROPN
stem-4332	76	22	.	.	PUNCT
stem-4332	77	1	if	if	SCONJ
stem-4332	77	2	he	he	PRON
stem-4332	77	3	was	be	AUX
stem-4332	77	4	right	right	ADJ
stem-4332	77	5	,	,	PUNCT
stem-4332	77	6	these	these	PRON
stem-4332	77	7	would	would	AUX
stem-4332	77	8	easily	easily	ADV
stem-4332	77	9	have	have	AUX
stem-4332	77	10	been	be	AUX
stem-4332	77	11	the	the	DET
stem-4332	77	12	biggest	big	ADJ
stem-4332	77	13	breakthroughs	breakthrough	NOUN
stem-4332	77	14	on	on	ADP
stem-4332	77	15	the	the	DET
stem-4332	77	16	problem	problem	NOUN
stem-4332	77	17	since	since	SCONJ
stem-4332	77	18	euclid	euclid	PROPN
stem-4332	77	19	2000	2000	NUM
stem-4332	77	20	years	year	NOUN
stem-4332	77	21	earlier	early	ADV
stem-4332	77	22	.	.	PUNCT
stem-4332	78	1	but	but	CCONJ
stem-4332	78	2	descartes	descartes	PROPN
stem-4332	78	3	could	could	AUX
stem-4332	78	4	n't	not	PART
stem-4332	78	5	prove	prove	VERB
stem-4332	78	6	either	either	PRON
stem-4332	78	7	of	of	ADP
stem-4332	78	8	those	those	DET
stem-4332	78	9	statements	statement	NOUN
stem-4332	78	10	.	.	PUNCT
stem-4332	79	1	instead	instead	ADV
stem-4332	79	2	,	,	PUNCT
stem-4332	79	3	he	he	PRON
stem-4332	79	4	wrote	write	VERB
stem-4332	79	5	"	"	PUNCT
stem-4332	79	6	as	as	ADP
stem-4332	79	7	for	for	ADP
stem-4332	79	8	me	i	PRON
stem-4332	79	9	,	,	PUNCT
stem-4332	79	10	i	i	PRON
stem-4332	79	11	judge	judge	VERB
stem-4332	79	12	that	that	SCONJ
stem-4332	79	13	one	one	PRON
stem-4332	79	14	can	can	AUX
stem-4332	79	15	find	find	VERB
stem-4332	79	16	real	real	ADJ
stem-4332	79	17	odd	odd	ADJ
stem-4332	79	18	perfect	perfect	ADJ
stem-4332	79	19	numbers	number	NOUN
stem-4332	79	20	.	.	PUNCT
stem-4332	80	1	but	but	CCONJ
stem-4332	80	2	whatever	whatever	DET
stem-4332	80	3	method	method	NOUN
stem-4332	80	4	you	you	PRON
stem-4332	80	5	use	use	VERB
stem-4332	80	6	,	,	PUNCT
stem-4332	80	7	it	it	PRON
stem-4332	80	8	takes	take	VERB
stem-4332	80	9	a	a	DET
stem-4332	80	10	long	long	ADJ
stem-4332	80	11	time	time	NOUN
stem-4332	80	12	to	to	PART
stem-4332	80	13	look	look	VERB
stem-4332	80	14	for	for	ADP
stem-4332	80	15	these	these	PRON
stem-4332	80	16	"	"	PUNCT
stem-4332	80	17	.	.	PUNCT
stem-4332	81	1	around	around	ADV
stem-4332	81	2	a	a	DET
stem-4332	81	3	hundred	hundred	NUM
stem-4332	81	4	years	year	NOUN
stem-4332	81	5	later	later	ADV
stem-4332	81	6	at	at	ADP
stem-4332	81	7	the	the	DET
stem-4332	81	8	st.petersburg	st.petersburg	PROPN
stem-4332	81	9	academy	academy	PROPN
stem-4332	81	10	,	,	PUNCT
stem-4332	81	11	the	the	DET
stem-4332	81	12	prussian	prussian	ADJ
stem-4332	81	13	mathematician	mathematician	ADJ
stem-4332	81	14	christian	christian	PROPN
stem-4332	81	15	goldbach	goldbach	NOUN
stem-4332	81	16	met	meet	VERB
stem-4332	81	17	a	a	DET
stem-4332	81	18	20	20	NUM
stem-4332	81	19	-	-	PUNCT
stem-4332	81	20	year	year	NOUN
stem-4332	81	21	-	-	PUNCT
stem-4332	81	22	old	old	ADJ
stem-4332	81	23	math	math	NOUN
stem-4332	81	24	prodigy	prodigy	NOUN
stem-4332	81	25	.	.	PUNCT
stem-4332	82	1	the	the	DET
stem-4332	82	2	two	two	NUM
stem-4332	82	3	stayed	stay	VERB
stem-4332	82	4	in	in	ADP
stem-4332	82	5	touch	touch	NOUN
stem-4332	82	6	corresponding	correspond	VERB
stem-4332	82	7	by	by	ADP
stem-4332	82	8	mail	mail	NOUN
stem-4332	82	9	,	,	PUNCT
stem-4332	82	10	and	and	CCONJ
stem-4332	82	11	in	in	ADP
stem-4332	82	12	1729	1729	NUM
stem-4332	82	13	,	,	PUNCT
stem-4332	82	14	goldbach	goldbach	NOUN
stem-4332	82	15	introduced	introduce	VERB
stem-4332	82	16	this	this	DET
stem-4332	82	17	young	young	ADJ
stem-4332	82	18	man	man	NOUN
stem-4332	82	19	to	to	ADP
stem-4332	82	20	the	the	DET
stem-4332	82	21	work	work	NOUN
stem-4332	82	22	of	of	ADP
stem-4332	82	23	fermat	fermat	PROPN
stem-4332	82	24	.	.	PUNCT
stem-4332	83	1	at	at	ADP
stem-4332	83	2	first	first	ADV
stem-4332	83	3	,	,	PUNCT
stem-4332	83	4	he	he	PRON
stem-4332	83	5	seemed	seem	VERB
stem-4332	83	6	indifferent	indifferent	ADJ
stem-4332	83	7	,	,	PUNCT
stem-4332	83	8	but	but	CCONJ
stem-4332	83	9	after	after	ADP
stem-4332	83	10	a	a	DET
stem-4332	83	11	little	little	ADJ
stem-4332	83	12	more	more	ADJ
stem-4332	83	13	prodding	prodding	NOUN
stem-4332	83	14	by	by	ADP
stem-4332	83	15	goldbach	goldbach	NOUN
stem-4332	83	16	he	he	PRON
stem-4332	83	17	became	become	VERB
stem-4332	83	18	passionate	passionate	ADJ
stem-4332	83	19	about	about	ADP
stem-4332	83	20	number	number	NOUN
stem-4332	83	21	theory	theory	NOUN
stem-4332	83	22	and	and	CCONJ
stem-4332	83	23	he	he	PRON
stem-4332	83	24	spent	spend	VERB
stem-4332	83	25	the	the	DET
stem-4332	83	26	next	next	ADJ
stem-4332	83	27	40	40	NUM
stem-4332	83	28	years	year	NOUN
stem-4332	83	29	working	work	VERB
stem-4332	83	30	on	on	ADP
stem-4332	83	31	different	different	ADJ
stem-4332	83	32	problems	problem	NOUN
stem-4332	83	33	in	in	ADP
stem-4332	83	34	the	the	DET
stem-4332	83	35	field	field	NOUN
stem-4332	83	36	among	among	ADP
stem-4332	83	37	them	they	PRON
stem-4332	83	38	was	be	AUX
stem-4332	83	39	the	the	DET
stem-4332	83	40	problem	problem	NOUN
stem-4332	83	41	of	of	ADP
stem-4332	83	42	perfect	perfect	ADJ
stem-4332	83	43	numbers	number	NOUN
stem-4332	83	44	.	.	PUNCT
stem-4332	84	1	this	this	DET
stem-4332	84	2	prodigy	prodigy	NOUN
stem-4332	84	3	's	's	PART
stem-4332	84	4	name	name	NOUN
stem-4332	84	5	was	be	AUX
stem-4332	84	6	leonhard	leonhard	PROPN
stem-4332	84	7	euler	euler	PROPN
stem-4332	84	8	.	.	PUNCT
stem-4332	84	9	euler	euler	PROPN
stem-4332	84	10	picked	pick	VERB
stem-4332	84	11	up	up	ADP
stem-4332	84	12	where	where	SCONJ
stem-4332	84	13	descartes	descartes	PROPN
stem-4332	84	14	had	have	AUX
stem-4332	84	15	left	leave	VERB
stem-4332	84	16	off	off	ADP
stem-4332	84	17	,	,	PUNCT
stem-4332	84	18	but	but	CCONJ
stem-4332	84	19	with	with	ADP
stem-4332	84	20	more	more	ADJ
stem-4332	84	21	success	success	NOUN
stem-4332	84	22	.	.	PUNCT
stem-4332	85	1	in	in	ADP
stem-4332	85	2	doing	do	VERB
stem-4332	85	3	so	so	ADV
stem-4332	85	4	,	,	PUNCT
stem-4332	85	5	he	he	PRON
stem-4332	85	6	made	make	VERB
stem-4332	85	7	three	three	NUM
stem-4332	85	8	breakthroughs	breakthrough	NOUN
stem-4332	85	9	on	on	ADP
stem-4332	85	10	this	this	DET
stem-4332	85	11	problem	problem	NOUN
stem-4332	85	12	.	.	PUNCT
stem-4332	86	1	first	first	ADV
stem-4332	86	2	in	in	ADP
stem-4332	86	3	1732	1732	NUM
stem-4332	86	4	,	,	PUNCT
stem-4332	86	5	he	he	PRON
stem-4332	86	6	discovered	discover	VERB
stem-4332	86	7	the	the	DET
stem-4332	86	8	eighth	eighth	ADJ
stem-4332	86	9	perfect	perfect	ADJ
stem-4332	86	10	number	number	NOUN
stem-4332	86	11	,	,	PUNCT
stem-4332	86	12	which	which	PRON
stem-4332	86	13	he	he	PRON
stem-4332	86	14	had	have	AUX
stem-4332	86	15	done	do	VERB
stem-4332	86	16	by	by	ADP
stem-4332	86	17	verifying	verify	VERB
stem-4332	86	18	that	that	SCONJ
stem-4332	86	19	(	(	PUNCT
stem-4332	86	20	231	231	NUM
stem-4332	86	21	−	−	NOUN
stem-4332	86	22	1	1	NUM
stem-4332	86	23	)	)	PUNCT
stem-4332	86	24	is	be	AUX
stem-4332	86	25	prime	prime	ADJ
stem-4332	86	26	.	.	PUNCT
stem-4332	87	1	just	just	ADV
stem-4332	87	2	as	as	SCONJ
stem-4332	87	3	mersenne	mersenne	PROPN
stem-4332	87	4	had	have	AUX
stem-4332	87	5	predicted	predict	VERB
stem-4332	87	6	.	.	PUNCT
stem-4332	88	1	for	for	ADP
stem-4332	88	2	his	his	PRON
stem-4332	88	3	other	other	ADJ
stem-4332	88	4	two	two	NUM
stem-4332	88	5	breakthroughs	breakthrough	NOUN
stem-4332	88	6	,	,	PUNCT
stem-4332	88	7	he	he	PRON
stem-4332	88	8	invented	invent	VERB
stem-4332	88	9	the	the	DET
stem-4332	88	10	sigma	sigma	PROPN
stem-4332	88	11	function	function	NOUN
stem-4332	88	12	.	.	PUNCT
stem-4332	89	1	293	293	NUM
stem-4332	89	2	journal	journal	NOUN
stem-4332	89	3	of	of	ADP
stem-4332	89	4	language	language	NOUN
stem-4332	89	5	,	,	PUNCT
stem-4332	89	6	literacy	literacy	NOUN
stem-4332	89	7	and	and	CCONJ
stem-4332	89	8	learning	learn	VERB
stem-4332	89	9	in	in	ADP
stem-4332	89	10	stem	stem	NOUN
stem-4332	89	11	education	education	NOUN
stem-4332	89	12	www	www	NOUN
stem-4332	89	13	.	.	PUNCT
stem-4332	90	1	grnjournal.us	grnjournal.us	X
stem-4332	90	2	the	the	DET
stem-4332	90	3	functions	function	NOUN
stem-4332	90	4	𝑑(𝑛	𝑑(𝑛	PROPN
stem-4332	90	5	)	)	PUNCT
stem-4332	90	6	𝐚𝐧𝐝	𝐚𝐧𝐝	ADJ
stem-4332	90	7	𝜎𝑘(𝑛	𝜎𝑘(𝑛	NUM
stem-4332	90	8	)	)	PUNCT
stem-4332	90	9	.	.	PUNCT
stem-4332	91	1	the	the	DET
stem-4332	91	2	function	function	NOUN
stem-4332	91	3	𝑑(𝑛	𝑑(𝑛	PROPN
stem-4332	91	4	)	)	PUNCT
stem-4332	91	5	is	be	AUX
stem-4332	91	6	the	the	DET
stem-4332	91	7	number	number	NOUN
stem-4332	91	8	of	of	ADP
stem-4332	91	9	divisors	divisor	NOUN
stem-4332	91	10	of	of	ADP
stem-4332	91	11	n	n	CCONJ
stem-4332	91	12	,	,	PUNCT
stem-4332	91	13	including	include	VERB
stem-4332	91	14	1	1	NUM
stem-4332	91	15	and	and	CCONJ
stem-4332	91	16	n	n	CCONJ
stem-4332	91	17	,	,	PUNCT
stem-4332	91	18	while	while	SCONJ
stem-4332	91	19	𝜎𝑘(𝑛	𝜎𝑘(𝑛	NUM
stem-4332	91	20	)	)	PUNCT
stem-4332	91	21	is	be	AUX
stem-4332	91	22	the	the	DET
stem-4332	91	23	sum	sum	NOUN
stem-4332	91	24	of	of	ADP
stem-4332	91	25	the	the	DET
stem-4332	91	26	kth	kth	PROPN
stem-4332	91	27	power	power	NOUN
stem-4332	91	28	of	of	ADP
stem-4332	91	29	the	the	DET
stem-4332	91	30	divisors	divisor	NOUN
stem-4332	91	31	of	of	ADP
stem-4332	91	32	n.	n.	NOUN
stem-4332	91	33	thus	thus	ADV
stem-4332	91	34	𝜎𝑘(𝑛	𝜎𝑘(𝑛	VERB
stem-4332	91	35	)	)	PUNCT
stem-4332	92	1	=	=	PUNCT
stem-4332	92	2	∑	∑	PROPN
stem-4332	92	3	𝑑𝑘	𝑑𝑘	INTJ
stem-4332	92	4	,	,	PUNCT
stem-4332	92	5	𝑑|𝑛	𝑑|𝑛	PROPN
stem-4332	92	6	𝑑(𝑛	𝑑(𝑛	PROPN
stem-4332	92	7	)	)	PUNCT
stem-4332	93	1	=	=	PUNCT
stem-4332	93	2	∑	∑	PUNCT
stem-4332	93	3	𝑙	𝑙	PROPN
stem-4332	93	4	𝑑|𝑛	𝑑|𝑛	NOUN
stem-4332	93	5	.	.	PUNCT
stem-4332	94	1	if	if	SCONJ
stem-4332	94	2	𝑛	𝑛	PRON
stem-4332	94	3	=	=	VERB
stem-4332	94	4	𝑝1	𝑝1	NOUN
stem-4332	94	5	𝑎1𝑝2	𝑎1𝑝2	PROPN
stem-4332	94	6	𝑎2	𝑎2	NOUN
stem-4332	94	7	⋯	⋯	PROPN
stem-4332	94	8	𝑝𝑙	𝑝𝑙	PROPN
stem-4332	94	9	𝑎𝑙	𝑎𝑙	NOUN
stem-4332	94	10	,	,	PUNCT
stem-4332	94	11	then	then	ADV
stem-4332	94	12	the	the	DET
stem-4332	94	13	divisors	divisor	NOUN
stem-4332	94	14	of	of	ADP
stem-4332	94	15	n	n	NUM
stem-4332	94	16	are	be	AUX
stem-4332	94	17	the	the	DET
stem-4332	94	18	number	number	NOUN
stem-4332	94	19	𝑝1	𝑝1	NOUN
stem-4332	94	20	𝑏1𝑝2	𝑏1𝑝2	PROPN
stem-4332	94	21	𝑏2	𝑏2	PROPN
stem-4332	94	22	⋯	⋯	PROPN
stem-4332	94	23	𝑝𝑙	𝑝𝑙	PROPN
stem-4332	94	24	𝑏𝑙	𝑏𝑙	PROPN
stem-4332	94	25	,	,	PUNCT
stem-4332	94	26	where	where	SCONJ
stem-4332	94	27	0	0	NUM
stem-4332	94	28	≤	≤	NUM
stem-4332	94	29	𝑏1	𝑏1	NOUN
stem-4332	94	30	≤	≤	PUNCT
stem-4332	94	31	𝑎1	𝑎1	ADV
stem-4332	94	32	,	,	PUNCT
stem-4332	94	33	0	0	NUM
stem-4332	94	34	≤	≤	PROPN
stem-4332	94	35	𝑏2	𝑏2	PROPN
stem-4332	94	36	≤	≤	PROPN
stem-4332	94	37	𝑎2	𝑎2	PROPN
stem-4332	94	38	,	,	PUNCT
stem-4332	94	39	⋯	⋯	ADP
stem-4332	94	40	0	0	NUM
stem-4332	94	41	≤	≤	NOUN
stem-4332	94	42	𝑏1	𝑏1	NOUN
stem-4332	94	43	≤	≤	PUNCT
stem-4332	94	44	𝑎𝑙.	𝑎𝑙.	NOUN
stem-4332	94	45	there	there	PRON
stem-4332	94	46	are	be	VERB
stem-4332	94	47	(	(	PUNCT
stem-4332	94	48	𝑎1	𝑎1	NOUN
stem-4332	94	49	+	+	CCONJ
stem-4332	94	50	1)(𝑎2	1)(𝑎2	NUM
stem-4332	94	51	+	+	CCONJ
stem-4332	94	52	1	1	NUM
stem-4332	94	53	)	)	PUNCT
stem-4332	94	54	⋯	⋯	VERB
stem-4332	94	55	(	(	PUNCT
stem-4332	94	56	𝑎𝑙	𝑎𝑙	NOUN
stem-4332	94	57	+	+	CCONJ
stem-4332	94	58	1	1	NUM
stem-4332	94	59	)	)	PUNCT
stem-4332	94	60	of	of	ADP
stem-4332	94	61	these	these	DET
stem-4332	94	62	numbers	number	NOUN
stem-4332	94	63	.	.	PUNCT
stem-4332	95	1	hence	hence	ADV
stem-4332	95	2	theorem	theorem	VERB
stem-4332	95	3	1	1	NUM
stem-4332	95	4	:	:	PUNCT
stem-4332	95	5	𝑑(𝑛	𝑑(𝑛	PROPN
stem-4332	95	6	)	)	PUNCT
stem-4332	95	7	=	=	SYM
stem-4332	96	1	∏(𝑎𝑖	∏(𝑎𝑖	PROPN
stem-4332	96	2	+	+	NUM
stem-4332	96	3	1	1	NUM
stem-4332	96	4	)	)	PUNCT
stem-4332	96	5	.	.	PUNCT
stem-4332	97	1	𝑙	𝑙	PUNCT
stem-4332	97	2	𝑖=1	𝑖=1	PROPN
stem-4332	97	3	more	more	ADV
stem-4332	97	4	generally	generally	ADV
stem-4332	97	5	,	,	PUNCT
stem-4332	97	6	if	if	SCONJ
stem-4332	97	7	𝑘	𝑘	PROPN
stem-4332	97	8	>	>	X
stem-4332	97	9	0	0	NUM
stem-4332	97	10	,	,	PUNCT
stem-4332	97	11	𝜎𝑘(𝑛	𝜎𝑘(𝑛	NUM
stem-4332	97	12	)	)	PUNCT
stem-4332	98	1	=	=	PUNCT
stem-4332	98	2	∑	∑	PROPN
stem-4332	98	3	∑	∑	PUNCT
stem-4332	98	4	⋯	⋯	VERB
stem-4332	98	5	∑	∑	PROPN
stem-4332	98	6	𝑝1	𝑝1	NOUN
stem-4332	98	7	𝑏1𝑘	𝑏1𝑘	PROPN
stem-4332	98	8	𝑝2	𝑝2	PROPN
stem-4332	98	9	𝑏2𝑘	𝑏2𝑘	PROPN
stem-4332	98	10	⋯	⋯	PROPN
stem-4332	98	11	𝑝𝑙	𝑝𝑙	PROPN
stem-4332	98	12	𝑏𝑙𝑘	𝑏𝑙𝑘	NOUN
stem-4332	98	13	=	=	PUNCT
stem-4332	98	14	∏(1	∏(1	PROPN
stem-4332	98	15	+	+	CCONJ
stem-4332	98	16	𝑝𝑖	𝑝𝑖	X
stem-4332	98	17	𝑘	𝑘	PROPN
stem-4332	98	18	+	+	NOUN
stem-4332	98	19	𝑝𝑖	𝑝𝑖	X
stem-4332	98	20	2𝑘	2𝑘	NUM
stem-4332	98	21	+	+	CCONJ
stem-4332	98	22	⋯	⋯	VERB
stem-4332	98	23	+	+	CCONJ
stem-4332	98	24	𝑝𝑖	𝑝𝑖	X
stem-4332	98	25	𝑎𝑖𝑘	𝑎𝑖𝑘	PROPN
stem-4332	98	26	)	)	PUNCT
stem-4332	98	27	.	.	PUNCT
stem-4332	99	1	𝑙	𝑙	X
stem-4332	99	2	𝑖=1	𝑖=1	PROPN
stem-4332	99	3	𝑎𝑙	𝑎𝑙	NOUN
stem-4332	99	4	𝑏𝑖	𝑏𝑖	ADP
stem-4332	99	5	𝑎2	𝑎2	PROPN
stem-4332	99	6	𝑏2	𝑏2	PROPN
stem-4332	99	7	𝑎1	𝑎1	PROPN
stem-4332	99	8	𝑏1	𝑏1	NOUN
stem-4332	99	9	hence	hence	ADV
stem-4332	99	10	theorem	theorem	VERB
stem-4332	99	11	2	2	NUM
stem-4332	99	12	:	:	PUNCT
stem-4332	99	13	𝜎𝑘(𝑛	𝜎𝑘(𝑛	NUM
stem-4332	99	14	)	)	PUNCT
stem-4332	99	15	=	=	SYM
stem-4332	99	16	∏	∏	PROPN
stem-4332	99	17	(	(	PUNCT
stem-4332	99	18	𝑝𝑖	𝑝𝑖	X
stem-4332	99	19	(	(	PUNCT
stem-4332	99	20	𝑎𝑖+1)𝑘	𝑎𝑖+1)𝑘	NOUN
stem-4332	99	21	−	−	PROPN
stem-4332	99	22	1	1	NUM
stem-4332	99	23	𝑝𝑖	𝑝𝑖	NOUN
stem-4332	99	24	𝑘	𝑘	PRON
stem-4332	99	25	−	−	PROPN
stem-4332	99	26	1	1	NUM
stem-4332	99	27	)	)	PUNCT
stem-4332	99	28	.	.	PUNCT
stem-4332	100	1	𝑙	𝑙	X
stem-4332	100	2	𝑖=1	𝑖=1	PUNCT
stem-4332	100	3	with	with	ADP
stem-4332	100	4	his	his	PRON
stem-4332	100	5	new	new	ADJ
stem-4332	100	6	function	function	NOUN
stem-4332	100	7	in	in	ADP
stem-4332	100	8	hand	hand	NOUN
stem-4332	100	9	,	,	PUNCT
stem-4332	100	10	euler	euler	PROPN
stem-4332	100	11	achieved	achieve	VERB
stem-4332	100	12	his	his	PRON
stem-4332	100	13	second	second	ADJ
stem-4332	100	14	breakthrough	breakthrough	NOUN
stem-4332	100	15	and	and	CCONJ
stem-4332	100	16	did	do	VERB
stem-4332	100	17	what	what	PRON
stem-4332	100	18	descartes	descarte	NOUN
stem-4332	100	19	could	could	AUX
stem-4332	100	20	n't	not	PART
stem-4332	100	21	.	.	PUNCT
stem-4332	101	1	he	he	PRON
stem-4332	101	2	proved	prove	VERB
stem-4332	101	3	that	that	SCONJ
stem-4332	101	4	every	every	DET
stem-4332	101	5	even	even	ADV
stem-4332	101	6	perfect	perfect	ADJ
stem-4332	101	7	number	number	NOUN
stem-4332	101	8	has	have	VERB
stem-4332	101	9	euclid	euclid	PROPN
stem-4332	101	10	's	's	PART
stem-4332	101	11	form	form	NOUN
stem-4332	101	12	.	.	PUNCT
stem-4332	102	1	this	this	DET
stem-4332	102	2	euclid	euclid	PROPN
stem-4332	102	3	−	−	PROPN
stem-4332	102	4	euler	euler	PROPN
stem-4332	102	5	theorem	theorem	PROPN
stem-4332	102	6	solved	solve	VERB
stem-4332	102	7	a	a	DET
stem-4332	102	8	1600	1600	NUM
stem-4332	102	9	-	-	PUNCT
stem-4332	102	10	year	year	NOUN
stem-4332	102	11	-	-	PUNCT
stem-4332	102	12	old	old	ADJ
stem-4332	102	13	problem	problem	NOUN
stem-4332	102	14	and	and	CCONJ
stem-4332	102	15	proved	prove	VERB
stem-4332	102	16	nicomachus	nicomachus	NOUN
stem-4332	102	17	's	's	PART
stem-4332	102	18	fourth	fourth	ADJ
stem-4332	102	19	conjecture	conjecture	NOUN
stem-4332	102	20	.	.	PUNCT
stem-4332	103	1	but	but	CCONJ
stem-4332	103	2	euler	euler	NOUN
stem-4332	103	3	was	be	AUX
stem-4332	103	4	n't	not	PART
stem-4332	103	5	done	do	VERB
stem-4332	103	6	yet	yet	ADV
stem-4332	103	7	.	.	PUNCT
stem-4332	104	1	he	he	PRON
stem-4332	104	2	also	also	ADV
stem-4332	104	3	wanted	want	VERB
stem-4332	104	4	to	to	PART
stem-4332	104	5	solve	solve	VERB
stem-4332	104	6	the	the	DET
stem-4332	104	7	problem	problem	NOUN
stem-4332	104	8	of	of	ADP
stem-4332	104	9	odd	odd	ADJ
stem-4332	104	10	perfect	perfect	ADJ
stem-4332	104	11	numbers	number	NOUN
stem-4332	104	12	.	.	PUNCT
stem-4332	105	1	so	so	ADV
stem-4332	105	2	for	for	ADP
stem-4332	105	3	his	his	PRON
stem-4332	105	4	third	third	ADJ
stem-4332	105	5	breakthrough	breakthrough	NOUN
stem-4332	105	6	,	,	PUNCT
stem-4332	105	7	he	he	PRON
stem-4332	105	8	set	set	VERB
stem-4332	105	9	out	out	ADP
stem-4332	105	10	to	to	PART
stem-4332	105	11	prove	prove	VERB
stem-4332	105	12	descartes	descarte	VERB
stem-4332	105	13	other	other	ADJ
stem-4332	105	14	statement	statement	NOUN
stem-4332	105	15	that	that	SCONJ
stem-4332	105	16	every	every	DET
stem-4332	105	17	odd	odd	ADJ
stem-4332	105	18	perfect	perfect	ADJ
stem-4332	105	19	number	number	NOUN
stem-4332	105	20	must	must	AUX
stem-4332	105	21	have	have	AUX
stem-4332	105	22	a	a	DET
stem-4332	105	23	specific	specific	ADJ
stem-4332	105	24	form	form	NOUN
stem-4332	105	25	.	.	PUNCT
stem-4332	106	1	but	but	CCONJ
stem-4332	106	2	he	he	PRON
stem-4332	106	3	could	could	AUX
stem-4332	106	4	not	not	PART
stem-4332	106	5	prove	prove	VERB
stem-4332	106	6	this	this	PRON
stem-4332	106	7	.	.	PUNCT
stem-4332	107	1	euler	euler	PROPN
stem-4332	107	2	wrote	write	VERB
stem-4332	107	3	:	:	PUNCT
stem-4332	107	4	"	"	PUNCT
stem-4332	107	5	whether	whether	SCONJ
stem-4332	107	6	there	there	PRON
stem-4332	107	7	are	be	VERB
stem-4332	107	8	any	any	DET
stem-4332	107	9	odd	odd	ADJ
stem-4332	107	10	perfect	perfect	ADJ
stem-4332	107	11	numbers	number	NOUN
stem-4332	107	12	is	be	AUX
stem-4332	107	13	the	the	DET
stem-4332	107	14	most	most	ADV
stem-4332	107	15	difficult	difficult	ADJ
stem-4332	107	16	question	question	NOUN
stem-4332	107	17	"	"	PUNCT
stem-4332	107	18	.	.	PUNCT
stem-4332	108	1	for	for	ADP
stem-4332	108	2	the	the	DET
stem-4332	108	3	next	next	ADJ
stem-4332	108	4	150	150	NUM
stem-4332	108	5	years	year	NOUN
stem-4332	108	6	very	very	ADV
stem-4332	108	7	little	little	ADJ
stem-4332	108	8	progress	progress	NOUN
stem-4332	108	9	was	be	AUX
stem-4332	108	10	made	make	VERB
stem-4332	108	11	and	and	CCONJ
stem-4332	108	12	no	no	DET
stem-4332	108	13	new	new	ADJ
stem-4332	108	14	perfect	perfect	ADJ
stem-4332	108	15	numbers	number	NOUN
stem-4332	108	16	were	be	AUX
stem-4332	108	17	discovered	discover	VERB
stem-4332	108	18	.	.	PUNCT
stem-4332	109	1	english	english	PROPN
stem-4332	109	2	mathematician	mathematician	PROPN
stem-4332	109	3	peter	peter	PROPN
stem-4332	109	4	barlow	barlow	PROPN
stem-4332	109	5	wrote	write	VERB
stem-4332	109	6	that	that	SCONJ
stem-4332	109	7	"	"	PUNCT
stem-4332	109	8	euler	euler	PROPN
stem-4332	109	9	’s	’s	PART
stem-4332	109	10	eighth	eighth	ADJ
stem-4332	109	11	perfect	perfect	ADJ
stem-4332	109	12	number	number	NOUN
stem-4332	109	13	is	be	AUX
stem-4332	109	14	the	the	DET
stem-4332	109	15	greatest	great	ADJ
stem-4332	109	16	that	that	PRON
stem-4332	109	17	ever	ever	ADV
stem-4332	109	18	will	will	AUX
stem-4332	109	19	be	be	AUX
stem-4332	109	20	discovered	discover	VERB
stem-4332	109	21	for	for	ADP
stem-4332	109	22	as	as	SCONJ
stem-4332	109	23	they	they	PRON
stem-4332	109	24	are	be	AUX
stem-4332	109	25	merely	merely	ADV
stem-4332	109	26	curious	curious	ADJ
stem-4332	109	27	without	without	ADP
stem-4332	109	28	being	be	AUX
stem-4332	109	29	useful	useful	ADJ
stem-4332	109	30	,	,	PUNCT
stem-4332	109	31	it	it	PRON
stem-4332	109	32	is	be	AUX
stem-4332	109	33	not	not	PART
stem-4332	109	34	likely	likely	ADJ
stem-4332	109	35	that	that	SCONJ
stem-4332	109	36	any	any	DET
stem-4332	109	37	person	person	NOUN
stem-4332	109	38	will	will	AUX
stem-4332	109	39	ever	ever	ADV
stem-4332	109	40	attempt	attempt	VERB
stem-4332	109	41	to	to	PART
stem-4332	109	42	find	find	VERB
stem-4332	109	43	one	one	NUM
stem-4332	109	44	beyond	beyond	ADP
stem-4332	109	45	it	it	PRON
stem-4332	109	46	"	"	PUNCT
stem-4332	109	47	.	.	PUNCT
stem-4332	110	1	but	but	CCONJ
stem-4332	110	2	barlow	barlow	PROPN
stem-4332	110	3	was	be	AUX
stem-4332	110	4	wrong	wrong	ADJ
stem-4332	110	5	.	.	PUNCT
stem-4332	111	1	mathematicians	mathematician	NOUN
stem-4332	111	2	kept	keep	VERB
stem-4332	111	3	pursuing	pursue	VERB
stem-4332	111	4	perfect	perfect	ADJ
stem-4332	111	5	numbers	number	NOUN
stem-4332	111	6	and	and	CCONJ
stem-4332	111	7	most	most	ADV
stem-4332	111	8	started	start	VERB
stem-4332	111	9	with	with	ADP
stem-4332	111	10	mersenne	mersenne	NOUN
stem-4332	111	11	's	's	PART
stem-4332	111	12	primes	prime	NOUN
stem-4332	111	13	list	list	NOUN
stem-4332	111	14	.	.	PUNCT
stem-4332	112	1	the	the	DET
stem-4332	112	2	next	next	ADJ
stem-4332	112	3	on	on	ADP
stem-4332	112	4	his	his	PRON
stem-4332	112	5	list	list	NOUN
stem-4332	112	6	was	be	AUX
stem-4332	112	7	267	267	NUM
stem-4332	112	8	−	−	NUM
stem-4332	112	9	1	1	NUM
stem-4332	112	10	.	.	PUNCT
stem-4332	113	1	but	but	CCONJ
stem-4332	113	2	in	in	ADP
stem-4332	113	3	1876	1876	NUM
stem-4332	113	4	edouard	edouard	PROPN
stem-4332	113	5	lucas	lucas	PROPN
stem-4332	113	6	the	the	DET
stem-4332	113	7	french	french	ADJ
stem-4332	113	8	mathematician	mathematician	NOUN
stem-4332	113	9	proved	prove	VERB
stem-4332	113	10	that	that	SCONJ
stem-4332	113	11	267	267	NUM
stem-4332	113	12	−	−	NUM
stem-4332	113	13	1	1	NUM
stem-4332	113	14	was	be	AUX
stem-4332	113	15	not	not	PART
stem-4332	113	16	prime	prime	ADJ
stem-4332	113	17	,	,	PUNCT
stem-4332	113	18	although	although	SCONJ
stem-4332	113	19	he	he	PRON
stem-4332	113	20	was	be	AUX
stem-4332	113	21	unable	unable	ADJ
stem-4332	113	22	to	to	PART
stem-4332	113	23	find	find	VERB
stem-4332	113	24	its	its	PRON
stem-4332	113	25	factors	factor	NOUN
stem-4332	113	26	.	.	PUNCT
stem-4332	114	1	27	27	NUM
stem-4332	114	2	years	year	NOUN
stem-4332	114	3	later	later	ADV
stem-4332	114	4	,	,	PUNCT
stem-4332	114	5	on	on	ADP
stem-4332	114	6	october	october	PROPN
stem-4332	114	7	31	31	NUM
stem-4332	114	8	,	,	PUNCT
stem-4332	114	9	1903	1903	NUM
stem-4332	114	10	frank	frank	PROPN
stem-4332	114	11	nelson	nelson	PROPN
stem-4332	114	12	cole	cole	PROPN
stem-4332	114	13	the	the	DET
stem-4332	114	14	american	american	ADJ
stem-4332	114	15	mathematician	mathematician	NOUN
stem-4332	114	16	gave	give	VERB
stem-4332	114	17	a	a	DET
stem-4332	114	18	talk	talk	NOUN
stem-4332	114	19	to	to	ADP
stem-4332	114	20	the	the	DET
stem-4332	114	21	american	american	PROPN
stem-4332	114	22	mathematical	mathematical	PROPN
stem-4332	114	23	society	society	NOUN
stem-4332	114	24	without	without	ADP
stem-4332	114	25	saying	say	VERB
stem-4332	114	26	a	a	DET
stem-4332	114	27	word	word	NOUN
stem-4332	114	28	,	,	PUNCT
stem-4332	114	29	he	he	PRON
stem-4332	114	30	walked	walk	VERB
stem-4332	114	31	to	to	ADP
stem-4332	114	32	one	one	NUM
stem-4332	114	33	side	side	NOUN
stem-4332	114	34	of	of	ADP
stem-4332	114	35	the	the	DET
stem-4332	114	36	blackboard	blackboard	NOUN
stem-4332	114	37	and	and	CCONJ
stem-4332	114	38	wrote	write	VERB
stem-4332	114	39	down	down	ADV
stem-4332	114	40	267	267	NUM
stem-4332	114	41	−	−	NOUN
stem-4332	114	42	1	1	NUM
stem-4332	114	43	=	=	SYM
stem-4332	114	44	147.573.952.589.676.412.927	147.573.952.589.676.412.927	NUM
stem-4332	114	45	.	.	PUNCT
stem-4332	115	1	he	he	PRON
stem-4332	115	2	then	then	ADV
stem-4332	115	3	walked	walk	VERB
stem-4332	115	4	to	to	ADP
stem-4332	115	5	the	the	DET
stem-4332	115	6	other	other	ADJ
stem-4332	115	7	side	side	NOUN
stem-4332	115	8	of	of	ADP
stem-4332	115	9	the	the	DET
stem-4332	115	10	blackboard	blackboard	NOUN
stem-4332	115	11	and	and	CCONJ
stem-4332	115	12	multiplied	multiply	VERB
stem-4332	115	13	193.707.721	193.707.721	NUM
stem-4332	115	14	times	time	NOUN
stem-4332	115	15	761.838.257.287	761.838.257.287	NUM
stem-4332	115	16	giving	give	VERB
stem-4332	115	17	the	the	DET
stem-4332	115	18	same	same	ADJ
stem-4332	115	19	answer	answer	NOUN
stem-4332	115	20	.	.	PUNCT
stem-4332	116	1	he	he	PRON
stem-4332	116	2	sat	sit	VERB
stem-4332	116	3	down	down	ADP
stem-4332	116	4	without	without	ADP
stem-4332	116	5	saying	say	VERB
stem-4332	116	6	a	a	DET
stem-4332	116	7	word	word	NOUN
stem-4332	116	8	and	and	CCONJ
stem-4332	116	9	the	the	DET
stem-4332	116	10	audience	audience	NOUN
stem-4332	116	11	erupted	erupt	VERB
stem-4332	116	12	in	in	ADP
stem-4332	116	13	applause	applause	NOUN
stem-4332	116	14	.	.	PUNCT
stem-4332	117	1	he	he	PRON
stem-4332	117	2	later	later	ADV
stem-4332	117	3	admitted	admit	VERB
stem-4332	117	4	it	it	PRON
stem-4332	117	5	took	take	VERB
stem-4332	117	6	him	he	PRON
stem-4332	117	7	three	three	NUM
stem-4332	117	8	years	year	NOUN
stem-4332	117	9	working	work	VERB
stem-4332	117	10	on	on	ADP
stem-4332	117	11	sundays	sunday	NOUN
stem-4332	117	12	to	to	PART
stem-4332	117	13	solve	solve	VERB
stem-4332	117	14	this	this	PRON
stem-4332	117	15	.	.	PUNCT
stem-4332	118	1	a	a	DET
stem-4332	118	2	modern	modern	ADJ
stem-4332	118	3	computer	computer	NOUN
stem-4332	118	4	could	could	AUX
stem-4332	118	5	solve	solve	VERB
stem-4332	118	6	this	this	PRON
stem-4332	118	7	in	in	ADP
stem-4332	118	8	a	a	DET
stem-4332	118	9	milliseconds	millisecond	NOUN
stem-4332	118	10	.	.	PUNCT
stem-4332	119	1	from	from	ADP
stem-4332	119	2	500	500	NUM
stem-4332	119	3	bc	bc	NOUN
stem-4332	119	4	until	until	ADP
stem-4332	119	5	1952	1952	NUM
stem-4332	119	6	people	people	NOUN
stem-4332	119	7	had	have	AUX
stem-4332	119	8	discovered	discover	VERB
stem-4332	119	9	just	just	ADV
stem-4332	119	10	12	12	NUM
stem-4332	119	11	mersenne	mersenne	NOUN
stem-4332	119	12	primes	prime	NOUN
stem-4332	119	13	and	and	CCONJ
stem-4332	119	14	therefore	therefore	ADV
stem-4332	119	15	only	only	ADV
stem-4332	119	16	12	12	NUM
stem-4332	119	17	perfect	perfect	ADJ
stem-4332	119	18	numbers	number	NOUN
stem-4332	119	19	.	.	PUNCT
stem-4332	120	1	the	the	DET
stem-4332	120	2	main	main	ADJ
stem-4332	120	3	difficulty	difficulty	NOUN
stem-4332	120	4	was	be	AUX
stem-4332	120	5	checking	check	VERB
stem-4332	120	6	whether	whether	SCONJ
stem-4332	120	7	large	large	ADJ
stem-4332	120	8	mersenne	mersenne	NOUN
stem-4332	120	9	numbers	number	NOUN
stem-4332	120	10	were	be	AUX
stem-4332	120	11	actually	actually	ADV
stem-4332	120	12	prime	prime	ADJ
stem-4332	120	13	.	.	PUNCT
stem-4332	121	1	but	but	CCONJ
stem-4332	121	2	in	in	ADP
stem-4332	121	3	1952	1952	NUM
stem-4332	121	4	,	,	PUNCT
stem-4332	121	5	american	american	ADJ
stem-4332	121	6	mathematician	mathematician	PROPN
stem-4332	121	7	raphael	raphael	PROPN
stem-4332	121	8	robinson	robinson	PROPN
stem-4332	121	9	wrote	write	VERB
stem-4332	121	10	a	a	DET
stem-4332	121	11	computer	computer	NOUN
stem-4332	121	12	294	294	NUM
stem-4332	121	13	journal	journal	NOUN
stem-4332	121	14	of	of	ADP
stem-4332	121	15	language	language	NOUN
stem-4332	121	16	,	,	PUNCT
stem-4332	121	17	literacy	literacy	NOUN
stem-4332	121	18	and	and	CCONJ
stem-4332	121	19	learning	learn	VERB
stem-4332	121	20	in	in	ADP
stem-4332	121	21	stem	stem	NOUN
stem-4332	121	22	education	education	NOUN
stem-4332	121	23	www	www	PROPN
stem-4332	121	24	.	.	PUNCT
stem-4332	122	1	grnjournal.us	grnjournal.us	PROPN
stem-4332	122	2	program	program	NOUN
stem-4332	122	3	to	to	PART
stem-4332	122	4	perform	perform	VERB
stem-4332	122	5	this	this	DET
stem-4332	122	6	task	task	NOUN
stem-4332	122	7	and	and	CCONJ
stem-4332	122	8	he	he	PRON
stem-4332	122	9	ran	run	VERB
stem-4332	122	10	it	it	PRON
stem-4332	122	11	on	on	ADP
stem-4332	122	12	the	the	DET
stem-4332	122	13	fastest	fast	ADJ
stem-4332	122	14	computer	computer	NOUN
stem-4332	122	15	at	at	ADP
stem-4332	122	16	the	the	DET
stem-4332	122	17	time	time	NOUN
stem-4332	122	18	,	,	PUNCT
stem-4332	122	19	the	the	DET
stem-4332	122	20	swac	swac	NOUN
stem-4332	122	21	.	.	PUNCT
stem-4332	123	1	within	within	ADP
stem-4332	123	2	10	10	NUM
stem-4332	123	3	months	month	NOUN
stem-4332	123	4	,	,	PUNCT
stem-4332	123	5	he	he	PRON
stem-4332	123	6	found	find	VERB
stem-4332	123	7	the	the	DET
stem-4332	123	8	next	next	ADJ
stem-4332	123	9	five	five	NUM
stem-4332	123	10	mersenne	mersenne	NOUN
stem-4332	123	11	primes	prime	NOUN
stem-4332	123	12	and	and	CCONJ
stem-4332	123	13	so	so	ADV
stem-4332	123	14	corresponding	corresponding	ADJ
stem-4332	123	15	perfect	perfect	ADJ
stem-4332	123	16	numbers	number	NOUN
stem-4332	123	17	.	.	PUNCT
stem-4332	124	1	and	and	CCONJ
stem-4332	124	2	over	over	ADP
stem-4332	124	3	the	the	DET
stem-4332	124	4	next	next	ADJ
stem-4332	124	5	50	50	NUM
stem-4332	124	6	years	year	NOUN
stem-4332	124	7	,	,	PUNCT
stem-4332	124	8	new	new	ADJ
stem-4332	124	9	mersenne	mersenne	NOUN
stem-4332	124	10	primes	prime	NOUN
stem-4332	124	11	were	be	AUX
stem-4332	124	12	discovered	discover	VERB
stem-4332	124	13	in	in	ADP
stem-4332	124	14	rapid	rapid	ADJ
stem-4332	124	15	succession	succession	NOUN
stem-4332	124	16	,	,	PUNCT
stem-4332	124	17	all	all	PRON
stem-4332	124	18	using	use	VERB
stem-4332	124	19	computers	computer	NOUN
stem-4332	124	20	.	.	PUNCT
stem-4332	125	1	the	the	DET
stem-4332	125	2	largest	large	ADJ
stem-4332	125	3	mersenne	mersenne	NOUN
stem-4332	125	4	prime	prime	NOUN
stem-4332	125	5	at	at	ADP
stem-4332	125	6	the	the	DET
stem-4332	125	7	end	end	NOUN
stem-4332	125	8	of	of	ADP
stem-4332	125	9	1952	1952	NUM
stem-4332	125	10	was	be	AUX
stem-4332	125	11	22281	22281	NUM
stem-4332	125	12	−	−	ADP
stem-4332	125	13	1	1	NUM
stem-4332	125	14	,	,	PUNCT
stem-4332	125	15	which	which	PRON
stem-4332	125	16	is	be	AUX
stem-4332	125	17	687	687	NUM
stem-4332	125	18	digits	digit	NOUN
stem-4332	125	19	long	long	ADV
stem-4332	125	20	.	.	PUNCT
stem-4332	126	1	by	by	ADP
stem-4332	126	2	the	the	DET
stem-4332	126	3	end	end	NOUN
stem-4332	126	4	of	of	ADP
stem-4332	126	5	1994	1994	NUM
stem-4332	126	6	,	,	PUNCT
stem-4332	126	7	the	the	DET
stem-4332	126	8	largest	large	ADJ
stem-4332	126	9	mersenne	mersenne	NOUN
stem-4332	126	10	prime	prime	NOUN
stem-4332	126	11	was	be	AUX
stem-4332	126	12	2859433	2859433	NUM
stem-4332	126	13	−	−	NOUN
stem-4332	126	14	1	1	NUM
stem-4332	126	15	,	,	PUNCT
stem-4332	126	16	which	which	PRON
stem-4332	126	17	is	be	AUX
stem-4332	126	18	258.716	258.716	NUM
stem-4332	126	19	digits	digit	NOUN
stem-4332	126	20	long	long	ADJ
stem-4332	126	21	.	.	PUNCT
stem-4332	127	1	nowadays	nowadays	ADV
stem-4332	127	2	there	there	PRON
stem-4332	127	3	are	be	VERB
stem-4332	127	4	51	51	NUM
stem-4332	127	5	mersenne	mersenne	NOUN
stem-4332	127	6	primes	prime	NOUN
stem-4332	127	7	.	.	PUNCT
stem-4332	128	1	in	in	ADP
stem-4332	128	2	2017	2017	NUM
stem-4332	128	3	church	church	NOUN
stem-4332	128	4	deacon	deacon	NOUN
stem-4332	128	5	john	john	PROPN
stem-4332	128	6	pace	pace	PROPN
stem-4332	128	7	discovered	discover	VERB
stem-4332	128	8	the	the	DET
stem-4332	128	9	50th	50th	ADJ
stem-4332	128	10	mersenne	mersenne	NOUN
stem-4332	128	11	prime	prime	NOUN
stem-4332	128	12	by	by	ADP
stem-4332	128	13	using	use	VERB
stem-4332	128	14	gimps	gimp	NOUN
stem-4332	128	15	.	.	PUNCT
stem-4332	129	1	the	the	DET
stem-4332	129	2	great	great	ADJ
stem-4332	129	3	internet	internet	NOUN
stem-4332	129	4	mersenne	mersenne	PROPN
stem-4332	129	5	prime	prime	PROPN
stem-4332	129	6	search	search	PROPN
stem-4332	129	7	(	(	PUNCT
stem-4332	129	8	gimps	gimp	NOUN
stem-4332	129	9	)	)	PUNCT
stem-4332	129	10	is	be	AUX
stem-4332	129	11	a	a	DET
stem-4332	129	12	collaborative	collaborative	ADJ
stem-4332	129	13	project	project	NOUN
stem-4332	129	14	of	of	ADP
stem-4332	129	15	volunteers	volunteer	NOUN
stem-4332	129	16	who	who	PRON
stem-4332	129	17	use	use	VERB
stem-4332	129	18	freely	freely	ADV
stem-4332	129	19	available	available	ADJ
stem-4332	129	20	software	software	NOUN
stem-4332	129	21	to	to	PART
stem-4332	129	22	search	search	VERB
stem-4332	129	23	for	for	ADP
stem-4332	129	24	mersenne	mersenne	NOUN
stem-4332	129	25	prime	prime	PROPN
stem-4332	129	26	numbers	number	NOUN
stem-4332	129	27	.	.	PUNCT
stem-4332	130	1	gimps	gimp	NOUN
stem-4332	130	2	was	be	AUX
stem-4332	130	3	founded	found	VERB
stem-4332	130	4	in	in	ADP
stem-4332	130	5	1996	1996	NUM
stem-4332	130	6	by	by	ADP
stem-4332	130	7	george	george	PROPN
stem-4332	130	8	woltman	woltman	PROPN
stem-4332	130	9	.	.	PUNCT
stem-4332	131	1	the	the	DET
stem-4332	131	2	number	number	NOUN
stem-4332	131	3	277232917	277232917	NUM
stem-4332	131	4	−	−	NOUN
stem-4332	131	5	1	1	NUM
stem-4332	131	6	is	be	AUX
stem-4332	131	7	more	more	ADJ
stem-4332	131	8	than	than	ADP
stem-4332	131	9	23	23	NUM
stem-4332	131	10	million	million	NUM
stem-4332	131	11	digits	digit	NOUN
stem-4332	131	12	long	long	ADV
stem-4332	131	13	,	,	PUNCT
stem-4332	131	14	and	and	CCONJ
stem-4332	131	15	it	it	PRON
stem-4332	131	16	was	be	AUX
stem-4332	131	17	also	also	ADV
stem-4332	131	18	the	the	DET
stem-4332	131	19	largest	large	ADJ
stem-4332	131	20	known	know	VERB
stem-4332	131	21	prime	prime	NOUN
stem-4332	131	22	at	at	ADP
stem-4332	131	23	the	the	DET
stem-4332	131	24	time	time	NOUN
stem-4332	131	25	.	.	PUNCT
stem-4332	132	1	a	a	DET
stem-4332	132	2	year	year	NOUN
stem-4332	132	3	later	later	ADV
stem-4332	132	4	,	,	PUNCT
stem-4332	132	5	the	the	DET
stem-4332	132	6	51st	51st	ADJ
stem-4332	132	7	mersenne	mersenne	NOUN
stem-4332	132	8	prime	prime	NOUN
stem-4332	132	9	was	be	AUX
stem-4332	132	10	discovered	discover	VERB
stem-4332	132	11	.	.	PUNCT
stem-4332	133	1	it	it	PRON
stem-4332	133	2	's	be	AUX
stem-4332	133	3	282589933	282589933	NUM
stem-4332	133	4	−	−	NOUN
stem-4332	133	5	1	1	NUM
stem-4332	133	6	,	,	PUNCT
stem-4332	133	7	and	and	CCONJ
stem-4332	133	8	this	this	DET
stem-4332	133	9	number	number	NOUN
stem-4332	133	10	has	have	VERB
stem-4332	133	11	24.862.048	24.862.048	NOUN
stem-4332	133	12	digits	digit	NOUN
stem-4332	133	13	.	.	PUNCT
stem-4332	134	1	the	the	DET
stem-4332	134	2	mersenne	mersenne	NOUN
stem-4332	134	3	primes	prime	NOUN
stem-4332	134	4	are	be	AUX
stem-4332	134	5	just	just	ADV
stem-4332	134	6	so	so	ADV
stem-4332	134	7	large	large	ADJ
stem-4332	134	8	and	and	CCONJ
stem-4332	134	9	rare	rare	ADJ
stem-4332	134	10	that	that	SCONJ
stem-4332	134	11	they	they	PRON
stem-4332	134	12	take	take	VERB
stem-4332	134	13	a	a	DET
stem-4332	134	14	lot	lot	NOUN
stem-4332	134	15	of	of	ADP
stem-4332	134	16	time	time	NOUN
stem-4332	134	17	and	and	CCONJ
stem-4332	134	18	computer	computer	NOUN
stem-4332	134	19	resources	resource	NOUN
stem-4332	134	20	to	to	PART
stem-4332	134	21	find	find	VERB
stem-4332	134	22	.	.	PUNCT
stem-4332	135	1	conclusion	conclusion	NOUN
stem-4332	135	2	to	to	ADP
stem-4332	135	3	this	this	DET
stem-4332	135	4	day	day	NOUN
stem-4332	135	5	,	,	PUNCT
stem-4332	135	6	the	the	DET
stem-4332	135	7	problem	problem	NOUN
stem-4332	135	8	of	of	ADP
stem-4332	135	9	odd	odd	ADJ
stem-4332	135	10	perfect	perfect	ADJ
stem-4332	135	11	numbers	number	NOUN
stem-4332	135	12	is	be	AUX
stem-4332	135	13	considered	consider	VERB
stem-4332	135	14	to	to	PART
stem-4332	135	15	be	be	AUX
stem-4332	135	16	the	the	DET
stem-4332	135	17	oldest	old	ADJ
stem-4332	135	18	unsolved	unsolved	ADJ
stem-4332	135	19	mathematical	mathematical	ADJ
stem-4332	135	20	problem	problem	NOUN
stem-4332	135	21	.	.	PUNCT
stem-4332	136	1	for	for	ADP
stem-4332	136	2	more	more	ADJ
stem-4332	136	3	than	than	ADP
stem-4332	136	4	2000	2000	NUM
stem-4332	136	5	years	year	NOUN
stem-4332	136	6	,	,	PUNCT
stem-4332	136	7	number	number	NOUN
stem-4332	136	8	theory	theory	NOUN
stem-4332	136	9	had	have	VERB
stem-4332	136	10	no	no	DET
stem-4332	136	11	practical	practical	ADJ
stem-4332	136	12	application	application	NOUN
stem-4332	136	13	.	.	PUNCT
stem-4332	137	1	mathematicians	mathematician	NOUN
stem-4332	137	2	simply	simply	ADV
stem-4332	137	3	followed	follow	VERB
stem-4332	137	4	their	their	PRON
stem-4332	137	5	curiosity	curiosity	NOUN
stem-4332	137	6	and	and	CCONJ
stem-4332	137	7	solved	solve	VERB
stem-4332	137	8	problems	problem	NOUN
stem-4332	137	9	that	that	PRON
stem-4332	137	10	seemed	seem	VERB
stem-4332	137	11	interesting	interesting	ADJ
stem-4332	137	12	to	to	ADP
stem-4332	137	13	them	they	PRON
stem-4332	137	14	,	,	PUNCT
stem-4332	137	15	proving	prove	VERB
stem-4332	137	16	one	one	NUM
stem-4332	137	17	result	result	NOUN
stem-4332	137	18	after	after	ADP
stem-4332	137	19	another	another	PRON
stem-4332	137	20	and	and	CCONJ
stem-4332	137	21	creating	create	VERB
stem-4332	137	22	the	the	DET
stem-4332	137	23	foundation	foundation	NOUN
stem-4332	137	24	of	of	ADP
stem-4332	137	25	today	today	NOUN
stem-4332	137	26	's	's	PART
stem-4332	137	27	mathematics	mathematic	NOUN
stem-4332	137	28	.	.	PUNCT
stem-4332	138	1	list	list	NOUN
stem-4332	138	2	of	of	ADP
stem-4332	138	3	references	reference	NOUN
stem-4332	138	4	:	:	PUNCT
stem-4332	138	5	1	1	X
stem-4332	138	6	.	.	PUNCT
stem-4332	139	1	g.	g.	PROPN
stem-4332	139	2	h.	h.	PROPN
stem-4332	140	1	hardy	hardy	PROPN
stem-4332	140	2	and	and	CCONJ
stem-4332	140	3	e.	e.	PROPN
stem-4332	140	4	m.	m.	PROPN
stem-4332	140	5	wright	wright	PROPN
stem-4332	140	6	,	,	PUNCT
stem-4332	140	7	an	an	DET
stem-4332	140	8	introduction	introduction	NOUN
stem-4332	140	9	to	to	ADP
stem-4332	140	10	the	the	DET
stem-4332	140	11	theory	theory	NOUN
stem-4332	140	12	of	of	ADP
stem-4332	140	13	number	number	NOUN
stem-4332	140	14	(	(	PUNCT
stem-4332	140	15	fourth	fourth	PROPN
stem-4332	140	16	edition	edition	NOUN
stem-4332	140	17	,	,	PUNCT
stem-4332	140	18	oxford	oxford	PROPN
stem-4332	140	19	,	,	PUNCT
stem-4332	140	20	1975	1975	NUM
stem-4332	140	21	)	)	PUNCT
stem-4332	140	22	.	.	PUNCT
stem-4332	141	1	2	2	X
stem-4332	141	2	.	.	X
stem-4332	141	3	i.	i.	PROPN
stem-4332	141	4	d.	d.	PROPN
stem-4332	141	5	mordukhai	mordukhai	PROPN
stem-4332	141	6	–	–	PUNCT
stem-4332	141	7	boltovsky	boltovsky	ADV
stem-4332	141	8	,	,	PUNCT
stem-4332	141	9	the	the	DET
stem-4332	141	10	ninth	ninth	ADJ
stem-4332	141	11	book	book	NOUN
stem-4332	141	12	of	of	ADP
stem-4332	141	13	euclid	euclid	PROPN
stem-4332	141	14	's	's	PART
stem-4332	141	15	elements	element	NOUN
stem-4332	141	16	(	(	PUNCT
stem-4332	141	17	russian	russian	PROPN
stem-4332	141	18	)	)	PUNCT
stem-4332	141	19	,	,	PUNCT
stem-4332	141	20	(	(	PUNCT
stem-4332	141	21	moscow	moscow	PROPN
stem-4332	141	22	,	,	PUNCT
stem-4332	141	23	1949	1949	NUM
stem-4332	141	24	)	)	PUNCT
stem-4332	141	25	3	3	NUM
stem-4332	141	26	.	.	PUNCT
stem-4332	141	27	джавлиева	джавлиева	VERB
stem-4332	142	1	г.р	г.р	PROPN
stem-4332	142	2	.	.	PROPN
stem-4332	143	1	on	on	ADP
stem-4332	143	2	the	the	DET
stem-4332	143	3	importance	importance	NOUN
stem-4332	143	4	of	of	ADP
stem-4332	143	5	historicism	historicism	NOUN
stem-4332	143	6	elements	element	NOUN
stem-4332	143	7	in	in	ADP
stem-4332	143	8	mathematics	mathematics	NOUN
stem-4332	143	9	lessons	lesson	NOUN
stem-4332	143	10	in	in	ADP
stem-4332	143	11	elementary	elementary	ADJ
stem-4332	143	12	grades	grade	NOUN
stem-4332	143	13	//the	//the	DET
stem-4332	143	14	american	american	PROPN
stem-4332	143	15	journal	journal	PROPN
stem-4332	143	16	of	of	ADP
stem-4332	143	17	applied	apply	VERB
stem-4332	143	18	sciences	science	NOUN
stem-4332	143	19	(	(	PUNCT
stem-4332	143	20	vol.15.09.2020).c.1	vol.15.09.2020).c.1	NOUN
stem-4332	143	21	-	-	PUNCT
stem-4332	143	22	10	10	NUM
stem-4332	143	23	.	.	PUNCT
stem-4332	143	24	4	4	NUM
stem-4332	143	25	.	.	NUM
stem-4332	143	26	джавлиева	джавлиева	VERB
stem-4332	144	1	г.р	г.р	PROPN
stem-4332	144	2	.	.	PROPN
stem-4332	144	3	интерактивные	интерактивные	PROPN
stem-4332	144	4	методы	методы	PROPN
stem-4332	145	1	в	в	PROPN
stem-4332	145	2	обучении	обучении	AUX
stem-4332	145	3	математике	математике	VERB
stem-4332	145	4	//	//	PROPN
stem-4332	145	5	journal	journal	PROPN
stem-4332	145	6	of	of	ADP
stem-4332	145	7	new	new	ADJ
stem-4332	145	8	century	century	NOUN
stem-4332	145	9	innovations	innovation	NOUN
stem-4332	145	10	.	.	PUNCT
stem-4332	146	1	volume	volume	NOUN
stem-4332	146	2	–	–	PUNCT
stem-4332	146	3	5	5	NUM
stem-4332	146	4	_	_	X
stem-4332	146	5	issue-1_may_2022.c.30	issue-1_may_2022.c.30	PROPN
stem-4332	146	6	-	-	PUNCT
stem-4332	146	7	35	35	NUM
stem-4332	146	8	.	.	PUNCT