id	sid	eid	entity	type
ejpam-245	1	1	4_245_jaroma.dvi	CARDINAL
ejpam-245	1	2	european journal	ORG
ejpam-245	1	3	2	CARDINAL
ejpam-245	1	4	3, 2009	DATE
ejpam-245	1	5	352-360	CARDINAL
ejpam-245	1	6	1307-5543	CARDINAL
ejpam-245	1	7	pepin	ORG
ejpam-245	1	8	john h. jaroma department	PERSON
ejpam-245	1	9	mathematics & physics	ORG
ejpam-245	1	10	ave maria university	ORG
ejpam-245	1	11	ave maria	PERSON
ejpam-245	1	12	florida	GPE
ejpam-245	1	13	34142	DATE
ejpam-245	1	14	united states	GPE
ejpam-245	2	1	pepin	PERSON
ejpam-245	3	1	the lucas-lehmer	ORG
ejpam-245	7	1	two	CARDINAL
ejpam-245	8	1	2000	CARDINAL
ejpam-245	8	2	11a41	CARDINAL
ejpam-245	8	3	11a51	CARDINAL
ejpam-245	8	4	11b39	CARDINAL
ejpam-245	8	5	pepin	PERSON
ejpam-245	8	6	lucas-lehmer	ORG
ejpam-245	9	1	1	CARDINAL
ejpam-245	9	2	22n + 1	DATE
ejpam-245	10	1	pierre de fermat	PERSON
ejpam-245	10	2	1601–1665	CARDINAL
ejpam-245	11	1	1732	DATE
ejpam-245	11	2	leonhard euler	PERSON
ejpam-245	12	1	352	CARDINAL
ejpam-245	12	2	2009	DATE
ejpam-245	13	1	john h. jaroma	PERSON
ejpam-245	14	1	j. pure	PERSON
ejpam-245	14	2	2	CARDINAL
ejpam-245	14	3	2009	DATE
ejpam-245	14	4	352-360	CARDINAL
ejpam-245	14	5	353	CARDINAL
ejpam-245	14	6	fermat	ORG
ejpam-245	15	1	today	DATE
ejpam-245	15	2	fermat	NORP
ejpam-245	15	3	4	CARDINAL
ejpam-245	16	1	fermat	NORP
ejpam-245	16	2	pepin	PERSON
ejpam-245	18	1	théophile pepin	PERSON
ejpam-245	18	2	1826–1904	CARDINAL
ejpam-245	18	3	3	CARDINAL
ejpam-245	18	4	−1	DATE
ejpam-245	19	1	1	CARDINAL
ejpam-245	19	2	11	CARDINAL
ejpam-245	19	3	15	CARDINAL
ejpam-245	20	1	mn	ORG
ejpam-245	20	2	2n−1	CARDINAL
ejpam-245	20	3	n ≥ 1	DATE
ejpam-245	21	1	marin mersenne	PERSON
ejpam-245	21	2	2	CARDINAL
ejpam-245	21	3	3	DATE
ejpam-245	21	4	5	DATE
ejpam-245	21	5	7	DATE
ejpam-245	21	6	13	DATE
ejpam-245	21	7	17	DATE
ejpam-245	21	8	19	DATE
ejpam-245	21	9	31	DATE
ejpam-245	21	10	67	DATE
ejpam-245	21	11	127	CARDINAL
ejpam-245	21	12	257	CARDINAL
ejpam-245	21	13	n ≤ 257	ORG
ejpam-245	22	1	more than 300 years	DATE
ejpam-245	23	1	only five	CARDINAL
ejpam-245	24	1	the lucas-lehmer	ORG
ejpam-245	26	1	mod mp	PERSON
ejpam-245	26	2	4	CARDINAL
ejpam-245	26	3	k ≥ 2	ORG
ejpam-245	26	4	r2 k−1	PERSON
ejpam-245	26	5	2	CARDINAL
ejpam-245	26	6	mod mp	PERSON
ejpam-245	26	7	0 ≤	QUANTITY
ejpam-245	27	1	1	CARDINAL
ejpam-245	27	2	13	CARDINAL
ejpam-245	27	3	14	CARDINAL
ejpam-245	28	1	pepin	PERSON
ejpam-245	29	1	two	CARDINAL
ejpam-245	30	1	two	CARDINAL
ejpam-245	31	1	10	CARDINAL
ejpam-245	31	2	pepin	PERSON
ejpam-245	31	3	3	CARDINAL
ejpam-245	31	4	derrick lehmer	PERSON
ejpam-245	31	5	fermat	NORP
ejpam-245	31	6	22n + 1	DATE
ejpam-245	31	7	fermat	NORP
ejpam-245	32	1	pepin	PERSON
ejpam-245	32	2	lehmer	GPE
ejpam-245	33	1	16	CARDINAL
ejpam-245	34	1	john h. jaroma	PERSON
ejpam-245	35	1	j. pure	PERSON
ejpam-245	35	2	2	CARDINAL
ejpam-245	35	3	2009	DATE
ejpam-245	35	4	352-360	CARDINAL
ejpam-245	35	5	354	CARDINAL
ejpam-245	35	6	pepin	PERSON
ejpam-245	35	7	2r	CARDINAL
ejpam-245	35	8	+ 1	DATE
ejpam-245	35	9	5	CARDINAL
ejpam-245	35	10	2	CARDINAL
ejpam-245	35	11	−1	DATE
ejpam-245	35	12	52	CARDINAL
ejpam-245	35	13	ti+1	ORG
ejpam-245	40	1	2	CARDINAL
ejpam-245	41	1	un	ORG
ejpam-245	42	1	1	CARDINAL
ejpam-245	42	2	0	CARDINAL
ejpam-245	42	3	1	CARDINAL
ejpam-245	43	1	2.1	CARDINAL
ejpam-245	44	1	2	CARDINAL
ejpam-245	44	2	0	CARDINAL
ejpam-245	44	3	1	CARDINAL
ejpam-245	45	1	2.2	CARDINAL
ejpam-245	45	2	2.1	CARDINAL
ejpam-245	45	3	2.2	CARDINAL
ejpam-245	45	4	linear	ORG
ejpam-245	45	5	2.3	CARDINAL
ejpam-245	45	6	2.4	CARDINAL
ejpam-245	46	1	un	ORG
ejpam-245	46	2	0	CARDINAL
ejpam-245	46	3	1	CARDINAL
ejpam-245	48	1	2.3	CARDINAL
ejpam-245	48	2	0	CARDINAL
ejpam-245	48	3	1	CARDINAL
ejpam-245	50	1	2.4	CARDINAL
ejpam-245	50	2	2	CARDINAL
ejpam-245	50	3	φ	ORG
ejpam-245	50	4	2	CARDINAL
ejpam-245	51	1	first	ORDINAL
ejpam-245	52	1	n ± 1.	PRODUCT
ejpam-245	53	1	3	CARDINAL
ejpam-245	54	1	3	CARDINAL
ejpam-245	55	1	john h. jaroma	PERSON
ejpam-245	56	1	j. pure	PERSON
ejpam-245	56	2	2	CARDINAL
ejpam-245	56	3	2009	DATE
ejpam-245	56	4	352-360	CARDINAL
ejpam-245	56	5	355	CARDINAL
ejpam-245	56	6	3.1	CARDINAL
ejpam-245	57	1	un	ORG
ejpam-245	57	2	1	CARDINAL
ejpam-245	57	3	2	CARDINAL
ejpam-245	58	1	1	CARDINAL
ejpam-245	59	1	-1	ORG
ejpam-245	59	2	1	CARDINAL
ejpam-245	61	1	0	CARDINAL
ejpam-245	62	1	legendre	ORG
ejpam-245	62	2	4q	CARDINAL
ejpam-245	62	3	2.1	CARDINAL
ejpam-245	62	4	2.2	CARDINAL
ejpam-245	63	1	3.2	CARDINAL
ejpam-245	65	1	up−σε	NORP
ejpam-245	65	2	q)≡	DATE
ejpam-245	66	1	ω(p	ORG
ejpam-245	66	2	un	ORG
ejpam-245	68	1	3.3	CARDINAL
ejpam-245	69	1	ω	ORDINAL
ejpam-245	69	2	un	ORG
ejpam-245	70	1	un	ORG
ejpam-245	70	2	k ∈	PERSON
ejpam-245	70	3	1	CARDINAL
ejpam-245	70	4	2	DATE
ejpam-245	71	1	un	ORG
ejpam-245	73	1	3.4	CARDINAL
ejpam-245	73	2	ω	ORG
ejpam-245	74	1	2k	CARDINAL
ejpam-245	75	1	λ(p	PERSON
ejpam-245	76	1	3.5	CARDINAL
ejpam-245	77	1	q)≡	DATE
ejpam-245	78	1	3.6	CARDINAL
ejpam-245	79	1	2rq∆.	DATE
ejpam-245	80	1	n ± 1	DATE
ejpam-245	81	1	john h. jaroma	PERSON
ejpam-245	82	1	j. pure	PERSON
ejpam-245	82	2	2	CARDINAL
ejpam-245	82	3	2009	DATE
ejpam-245	82	4	352-360	CARDINAL
ejpam-245	82	5	356 4	DATE
ejpam-245	82	6	two	CARDINAL
ejpam-245	82	7	first	ORDINAL
ejpam-245	83	1	1877	DATE
ejpam-245	84	1	pepin	PERSON
ejpam-245	84	2	4.1	CARDINAL
ejpam-245	85	1	pepin	PERSON
ejpam-245	85	2	fermat	ORG
ejpam-245	85	3	22n	CARDINAL
ejpam-245	85	4	1	CARDINAL
ejpam-245	85	5	5	CARDINAL
ejpam-245	85	6	2	CARDINAL
ejpam-245	86	1	pepin	PERSON
ejpam-245	86	2	10	CARDINAL
ejpam-245	86	3	5	CARDINAL
ejpam-245	86	4	pepin	ORG
ejpam-245	86	5	françois proth	PERSON
ejpam-245	86	6	1852 – 1879	DATE
ejpam-245	86	7	1876	DATE
ejpam-245	86	8	1878	DATE
ejpam-245	86	9	3	CARDINAL
ejpam-245	86	10	5	CARDINAL
ejpam-245	86	11	4.1	CARDINAL
ejpam-245	87	1	8	CARDINAL
ejpam-245	88	1	9	CARDINAL
ejpam-245	89	1	1842	DATE
ejpam-245	89	2	1891	DATE
ejpam-245	89	3	5	CARDINAL
ejpam-245	90	1	5	CARDINAL
ejpam-245	90	2	1879	DATE
ejpam-245	90	3	6	CARDINAL
ejpam-245	91	1	pepin	PERSON
ejpam-245	92	1	16	CARDINAL
ejpam-245	93	1	pepin	ORG
ejpam-245	93	2	4.2	CARDINAL
ejpam-245	94	1	pepin	PERSON
ejpam-245	94	2	fermat	ORG
ejpam-245	94	3	22n	CARDINAL
ejpam-245	94	4	3	CARDINAL
ejpam-245	95	1	1878	DATE
ejpam-245	96	1	lucas	PERSON
ejpam-245	96	2	two	CARDINAL
ejpam-245	96	3	2n	CARDINAL
ejpam-245	96	4	1	CARDINAL
ejpam-245	96	5	5	CARDINAL
ejpam-245	97	1	john h. jaroma	PERSON
ejpam-245	98	1	j. pure	PERSON
ejpam-245	98	2	2	CARDINAL
ejpam-245	98	3	2009	DATE
ejpam-245	98	4	352-360	CARDINAL
ejpam-245	98	5	357	CARDINAL
ejpam-245	99	1	1930	DATE
ejpam-245	99	2	d. h. lehmer	ORG
ejpam-245	99	3	3	CARDINAL
ejpam-245	100	1	r. d. carmichael	NORP
ejpam-245	100	2	2	CARDINAL
ejpam-245	101	1	two	CARDINAL
ejpam-245	103	1	3	CARDINAL
ejpam-245	104	1	today	DATE
ejpam-245	105	1	3	CARDINAL
ejpam-245	105	2	13	CARDINAL
ejpam-245	105	3	4	CARDINAL
ejpam-245	106	1	4.3	CARDINAL
ejpam-245	106	2	lucas-lehmer	ORG
ejpam-245	106	3	mn	ORG
ejpam-245	106	4	2n	CARDINAL
ejpam-245	107	1	1	CARDINAL
ejpam-245	107	2	1)st	CARDINAL
ejpam-245	107	3	4	CARDINAL
ejpam-245	107	4	14	DATE
ejpam-245	107	5	194	CARDINAL
ejpam-245	107	6	37634	DATE
ejpam-245	107	7	1416317954	DATE
ejpam-245	109	1	2	CARDINAL
ejpam-245	109	2	5	CARDINAL
ejpam-245	109	3	pepin	ORG
ejpam-245	109	4	pepin	PERSON
ejpam-245	110	1	3	CARDINAL
ejpam-245	111	1	3n+ 1	DATE
ejpam-245	112	1	5.1	CARDINAL
ejpam-245	112	2	one	CARDINAL
ejpam-245	113	1	john h. jaroma	PERSON
ejpam-245	114	1	j. pure	PERSON
ejpam-245	114	2	2	CARDINAL
ejpam-245	114	3	2009	DATE
ejpam-245	114	4	352-360	CARDINAL
ejpam-245	114	5	358	CARDINAL
ejpam-245	114	6	5.1	CARDINAL
ejpam-245	116	1	1	CARDINAL
ejpam-245	117	1	2.4	CARDINAL
ejpam-245	117	2	+ 1	DATE
ejpam-245	118	1	3	CARDINAL
ejpam-245	118	2	3n + 1	DATE
ejpam-245	119	1	vfn−1	PERSON
ejpam-245	119	2	2	CARDINAL
ejpam-245	119	3	3	CARDINAL
ejpam-245	119	4	2	CARDINAL
ejpam-245	120	1	4.2	CARDINAL
ejpam-245	120	2	5.2	CARDINAL
ejpam-245	121	1	3	CARDINAL
ejpam-245	123	1	5.1	CARDINAL
ejpam-245	123	2	5.2	CARDINAL
ejpam-245	124	1	pepin	PERSON
ejpam-245	124	2	fermat	ORG
ejpam-245	124	3	22n + 1	DATE
ejpam-245	124	4	1	CARDINAL
ejpam-245	125	1	4	CARDINAL
ejpam-245	125	2	3	CARDINAL
ejpam-245	127	1	3	CARDINAL
ejpam-245	128	1	4q	CARDINAL
ejpam-245	128	2	12	CARDINAL
ejpam-245	128	3	4	CARDINAL
ejpam-245	128	4	22n + 1	DATE
ejpam-245	128	5	2	CARDINAL
ejpam-245	128	6	1	CARDINAL
ejpam-245	128	7	16	CARDINAL
ejpam-245	128	8	1	CARDINAL
ejpam-245	129	1	3	CARDINAL
ejpam-245	129	2	3 22n	CARDINAL
ejpam-245	129	3	22n	CARDINAL
ejpam-245	129	4	3−1	CARDINAL
ejpam-245	129	5	22n	CARDINAL
ejpam-245	129	6	2	CARDINAL
ejpam-245	129	7	1	CARDINAL
ejpam-245	130	1	3	CARDINAL
ejpam-245	131	1	3	CARDINAL
ejpam-245	131	2	22n + 1	DATE
ejpam-245	131	3	3−1 2	CARDINAL
ejpam-245	131	4	−1	DATE
ejpam-245	132	1	1	CARDINAL
ejpam-245	132	2	3.2	CARDINAL
ejpam-245	133	1	6=	CARDINAL
ejpam-245	133	2	lemma 3.5	ORG
ejpam-245	134	1	3	DATE
ejpam-245	134	2	22n	CARDINAL
ejpam-245	134	3	1	CARDINAL
ejpam-245	135	1	3.3	CARDINAL
ejpam-245	135	2	22n−r	CARDINAL
ejpam-245	135	3	r.	NORP
ejpam-245	135	4	3.3	CARDINAL
ejpam-245	136	1	3.4	CARDINAL
ejpam-245	136	2	vfn−1 2	FAC
ejpam-245	138	1	5.1	CARDINAL
ejpam-245	140	1	lemma 3.3	ORG
ejpam-245	140	2	ω(fn	ORG
ejpam-245	140	3	22n	CARDINAL
ejpam-245	141	1	3.1	CARDINAL
ejpam-245	142	1	ω(fn	ORG
ejpam-245	142	2	22n	CARDINAL
ejpam-245	142	3	1	CARDINAL
ejpam-245	142	4	3.6	CARDINAL
ejpam-245	143	1	4	CARDINAL
ejpam-245	143	2	14	DATE
ejpam-245	143	3	194	CARDINAL
ejpam-245	143	4	37634	DATE
ejpam-245	143	5	1416317954	DATE
ejpam-245	144	1	4.3	CARDINAL
ejpam-245	144	2	john h. jaroma	PERSON
ejpam-245	145	1	j. pure	PERSON
ejpam-245	145	2	2	CARDINAL
ejpam-245	145	3	2009	DATE
ejpam-245	145	4	352-360	CARDINAL
ejpam-245	145	5	359	CARDINAL
ejpam-245	145	6	2	CARDINAL
ejpam-245	146	1	first	ORDINAL
ejpam-245	146	2	3	CARDINAL
ejpam-245	147	1	2	CARDINAL
ejpam-245	147	2	2qn	ORDINAL
ejpam-245	148	1	5.2	CARDINAL
ejpam-245	149	1	4	CARDINAL
ejpam-245	150	1	4.3	CARDINAL
ejpam-245	150	2	2	CARDINAL
ejpam-245	150	3	4	CARDINAL
ejpam-245	151	1	5.2	CARDINAL
ejpam-245	151	2	k ∈	PERSON
ejpam-245	151	3	1	CARDINAL
ejpam-245	151	4	2	DATE
ejpam-245	153	1	mn	ORG
ejpam-245	153	2	1)st	CARDINAL
ejpam-245	153	3	4	CARDINAL
ejpam-245	153	4	14	DATE
ejpam-245	153	5	194	CARDINAL
ejpam-245	153	6	37634	DATE
ejpam-245	153	7	1416317954	DATE
ejpam-245	154	1	mn	GPE
ejpam-245	155	1	4.3	CARDINAL
ejpam-245	155	2	5.3	CARDINAL
ejpam-245	156	1	lucas-lehmer	ORG
ejpam-245	156	2	2n	CARDINAL
ejpam-245	157	1	1	CARDINAL
ejpam-245	157	2	2	CARDINAL
ejpam-245	159	1	2	CARDINAL
ejpam-245	159	2	−1	DATE
ejpam-245	159	3	6	CARDINAL
ejpam-245	159	4	σ	CARDINAL
ejpam-245	159	5	1	CARDINAL
ejpam-245	159	6	−1	DATE
ejpam-245	160	1	5.2	CARDINAL
ejpam-245	161	1	3	CARDINAL
ejpam-245	162	1	1	CARDINAL
ejpam-245	162	2	d. m. burton	PERSON
ejpam-245	162	3	6th	ORDINAL
ejpam-245	162	4	mcgraw-hill	ORG
ejpam-245	162	5	new york	GPE
ejpam-245	162	6	2005	DATE
ejpam-245	163	1	2	CARDINAL
ejpam-245	163	2	αn±βn	DATE
ejpam-245	163	3	ann	PERSON
ejpam-245	164	1	2nd ser	DATE
ejpam-245	165	1	15	CARDINAL
ejpam-245	165	2	30–70	CARDINAL
ejpam-245	165	3	1913	DATE
ejpam-245	166	1	3	CARDINAL
ejpam-245	166	2	ann	PERSON
ejpam-245	167	1	31	CARDINAL
ejpam-245	168	1	419–448	CARDINAL
ejpam-245	168	2	1930	DATE
ejpam-245	169	1	4	CARDINAL
ejpam-245	169	2	d. h. lemer	PERSON
ejpam-245	169	3	mersenne	PERSON
ejpam-245	169	4	j. lon	PERSON
ejpam-245	171	1	10	CARDINAL
ejpam-245	171	2	162–165	CARDINAL
ejpam-245	172	1	5	CARDINAL
ejpam-245	172	2	lucas	PERSON
ejpam-245	172	3	théorie des fonctions numériques simplement périodiques	ORG
ejpam-245	172	4	amer	PERSON
ejpam-245	173	1	j. math	PERSON
ejpam-245	174	1	1	CARDINAL
ejpam-245	174	2	184–240	CARDINAL
ejpam-245	174	3	289–321	CARDINAL
ejpam-245	175	1	6	CARDINAL
ejpam-245	175	2	lucas	PERSON
ejpam-245	175	3	453	CARDINAL
ejpam-245	175	4	nouv	GPE
ejpam-245	176	1	cor	ORG
ejpam-245	177	1	5	CARDINAL
ejpam-245	177	2	1879	DATE
ejpam-245	178	1	john h. jaroma	PERSON
ejpam-245	179	1	j. pure	PERSON
ejpam-245	179	2	2	CARDINAL
ejpam-245	179	3	2009	DATE
ejpam-245	179	4	352-360	DATE
ejpam-245	179	5	360	CARDINAL
ejpam-245	180	1	t. pepin	PERSON
ejpam-245	180	2	sur la formule	ORG
ejpam-245	180	3	22n + 1	DATE
ejpam-245	182	1	acad	PERSON
ejpam-245	183	1	sci	ORG
ejpam-245	183	2	85	CARDINAL
ejpam-245	183	3	329–331	CARDINAL
ejpam-245	183	4	1877	DATE
ejpam-245	184	1	8	CARDINAL
ejpam-245	184	2	f. proth	PERSON
ejpam-245	184	3	énoncés de divers théorèmes sur les nombres	ORG
ejpam-245	186	1	acad	PERSON
ejpam-245	187	1	sci	ORG
ejpam-245	188	1	83	CARDINAL
ejpam-245	189	1	9	CARDINAL
ejpam-245	189	2	f. proth	PERSON
ejpam-245	191	1	acad	PERSON
ejpam-245	192	1	sci	ORG
ejpam-245	193	1	87	CARDINAL
ejpam-245	193	2	1878	DATE
ejpam-245	194	1	10	CARDINAL
ejpam-245	194	2	new york	GPE
ejpam-245	194	3	1996	DATE
ejpam-245	195	1	11	CARDINAL
ejpam-245	195	2	n. robbins	PERSON
ejpam-245	195	3	wm	PERSON
ejpam-245	195	4	c. brown	PERSON
ejpam-245	195	5	1993	DATE
ejpam-245	196	1	12	CARDINAL
ejpam-245	196	2	k. h. rosen	PERSON
ejpam-245	196	3	4th	ORDINAL
ejpam-245	196	4	addison wesley longman	PERSON
ejpam-245	196	5	2000	DATE
ejpam-245	197	1	13	CARDINAL
ejpam-245	197	2	m. rosen	PERSON
ejpam-245	197	3	amer	PERSON
ejpam-245	198	1	mon	PERSON
ejpam-245	199	1	95	CARDINAL
ejpam-245	199	2	855–856	CARDINAL
ejpam-245	199	3	1988	DATE
ejpam-245	200	1	14	CARDINAL
ejpam-245	200	2	pws,	ORG
ejpam-245	200	3	boston	GPE
ejpam-245	200	4	1996	DATE
ejpam-245	201	1	15	CARDINAL
ejpam-245	201	2	j. j.	PERSON
ejpam-245	201	3	nine	CARDINAL
ejpam-245	201	4	cambridge	GPE
ejpam-245	201	5	univ.	ORG
ejpam-245	202	1	cambridge	GPE
ejpam-245	202	2	2005	DATE
ejpam-245	203	1	16	CARDINAL
ejpam-245	203	2	h. c. williams	PERSON
ejpam-245	203	3	john wiley & sons	ORG
ejpam-245	203	4	new york	GPE
ejpam-245	203	5	1998	DATE