M2874941 Mersenne number exponent details

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M2874941

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is 2 ^2874941 - 1

has 865444 decimal digits

takes 0.222 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	526D3118FD231296	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	20.7326	67.6471%	5000000	200000000	1.7498	9.1807%	22.4823	70.6173%	2.9702%
PrimeNet	2⁵⁹	0.0267	62.7119%	13000	240000	0.0028	2.9975%	0.0296	63.8296%	1.1177%
GPU72	2⁶³	0.5551	65.0794%	16000	280000	0.0034	1.8702%	0.5586	65.7324%	0.6531%
Difference	+5	+20.1774	+2.5677%	+4984000	+199720000	+1.7464	+7.3106%	+21.9238	+4.8849%	+4.8849%

Known prime factors (1 factor, 75.9 bits, 0.00263852% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2874941	68373249400249906485391	23	75.856	11891243924701395 3 × 5 × 31 × 173 × 147818309711	2021-04-20	173	147818309711	5,159.0	901.94	1,684.6

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-28T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.245%
2009-07-03T00:56:00	Carsten Kossendey	leela	15000	161250		-		-	-	0.003	-	-	0.723%
2010-12-23T00:29:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.272%
2011-01-22T22:18:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.544%
2011-02-07T10:45:00	markr	tiny	125000	2812500		-		-	-	0.030	-	-	2.793%
2016-09-17T03:20:36	Jocelyn Larouche	low 4M	166375	3093750	6	-		-	-	0.036	-	-	3.000%
2016-12-21T00:33:39	Jocelyn Larouche	low 4M	199650	199650		-		-	-	0.022	-	-	1.234%
2017-04-13T02:13:58	Jocelyn Larouche	low 4M	332750	3327500	6	-		-	-	0.056	-	-	3.365%
2018-01-22T19:54:02	Jocelyn Larouche	low 4M	574992	574992		-		-	-	0.064	-	-	2.015%
2018-09-03T21:22:22	Jocelyn Larouche	low 4M	739990	1479980	6	-		-	-	0.087	-	-	2.872%
2018-09-05T22:38:04	Jocelyn Larouche	low 4M	739990	2219970	4	-		-	-	0.092	-	-	3.250%
2018-09-12T23:00:20	Jocelyn Larouche	low 4M	739990	3699950		-		-	-	0.101	-	-	3.731%
2019-10-23T02:43:09	masser	Manual testing	2880000	28800000	12	-		-	-	0.481	-	-	6.428%
2020-03-03T02:34:23	masser	Manual testing	5000000	200000000	12	-		-	-	1.750	-	-	9.181%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-04-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.027	-	-
2016-02-23T16:29:23	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.027	-	-
2009-02-12T06:13:00	Sturle Sunde	gopher.ifi	2⁶⁰	2⁶¹		-	-	0.053	-	-
2012-01-22T04:52:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.107	-	-
2013-01-07T13:47:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.341	-	-
2015-04-21T09:21:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.683	-	-
2015-04-21T09:21:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.300	-	-
2016-02-19T04:21:38	Yxinity	Manual testing	2⁶⁵	2⁶⁶		-	-	2.599	-	-
2017-11-12T17:07:20	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.199	-	-
2019-01-09T01:10:00	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.40	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.358 GHz-days
Estimated T-Level:	3.950

Digits	B1	Curves	Complete	FacMiss
20	11000	79 / 100	0.790	45.204%
25	50000	79 / 280	0.282	75.379%

New Calculation Method

Total ECM effort:	8.358 GHz-days
Estimated T-Level:	3.950

Digits	B1	Complete	FacMiss
20	11000	2.564	7.700%
25	50000	0.232	79.311%
30	250000	0.014	98.582%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		66	6.906
50000	5000000	68373249400249906485391	6	0.628
50000	6450000		7	0.825

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-24T22:58:00	willreid	jing	50000	5000000						3	0.314
2011-01-07T14:04:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.314
2013-05-03T06:23:00	Pool Party	St.P.p	50000	5000000						3	0.314
2015-07-22T10:14:00	Adel El-Atawy	MainMTV	50000	5000000						3	0.314
2016-09-14T22:50:02	Ismo Laitela		50000	5000000						3	0.314
2019-06-04T11:40:48	furkell	furkell1	50000	5000000						3	0.314
2020-08-05T00:30:17	GAN	LMS-13	50000	5000000						3	0.314
2020-08-13T03:53:09	GAN	LMS-02	50000	5000000						3	0.314
2020-09-02T14:48:49	daveward2005	Dave2	50000	5000000						7	0.732
2020-10-06T15:07:31	mnd9	75204b	50000	5000000						7	0.732
2020-11-01T19:47:56	IanGlencross	glenx24	50000	5000000						7	0.732
2020-12-07T05:58:29	IanGlencross	glenx24	50000	5000000						7	0.732
2021-01-08T17:02:31	lycorn	colab_S	50000	6450000						7	0.825
2021-02-13T13:23:58	arachnotron	AsusLaptop	50000	5000000						7	0.732
2021-03-13T14:56:08	Zenzoma	AMD3970X	50000	5000000						7	0.732
2021-04-20T22:40:20	mnd9	50869	50000	5000000	68373249400249906485391	75.856	6	2	3168991564766281	6	0.628

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-06-01T00:00:00	ANONYMOUS	v4_computers	526D3118FD231296	0.222
1999-07-27T00:00:00	ANONYMOUS	v4_computers	526D3118FD231296	0.222
2018-09-22T19:05:58	kkmrkkblmbrbk	old	526D3118FD231296	0.222

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-04-24T07:22:35

Klaus Nordmann

no1

68373249400249906485391

76E28806BE638F__

2021-04-30T19:13:50

Kirill Frolov

shodan1

68373249400249906485391

76E28806BE638F91

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 5000000, B2 = 200000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 2880000, B2 = 28800000 (P-1 stage 2)

B1 = 2880000 (P-1 stage 1)

B1 = 739990, B2 = 3699950 (P-1 stage 2)

B1 = 739990, B2 = 2219970 (P-1 stage 2)

B1 = 739990, B2 = 1479980 (P-1 stage 2)

B1 = 739990 (P-1 stage 1)

B1 = 574992 (P-1 stage 1)

B1 = 332750, B2 = 3327500 (P-1 stage 2)

B1 = 332750 (P-1 stage 1)

B1 = 166375, B2 = 3093750 (P-1 stage 2)

B1 = 125000, B2 = 2812500 (P-1 stage 2)

B1 = 199650 (P-1 stage 1)

B1 = 166375 (P-1 stage 1)

B1 = 125000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 15000, B2 = 161250 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10¹

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10⁴

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10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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10⁹

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TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-04-30T19:13:50+00:00

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront