M2870587 Mersenne number exponent details

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M2870587

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>>>

is 2 ^2870587 - 1

has 864133 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	F32F6F64401ED076	double-checked
PRP	488CC9B80B262377	verified PRP

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	20.7640	67.6471%	5000000	200000000	1.7498	9.1794%	22.5138	70.6169%	2.9698%
PrimeNet	2⁵⁹	0.0268	62.7119%	13000	240000	0.0028	2.9967%	0.0296	63.8293%	1.1174%
GPU72	2⁶³	0.5560	65.0794%	16000	280000	0.0034	1.8696%	0.5594	65.7322%	0.6529%
Difference	+5	+20.2080	+2.5677%	+4984000	+199720000	+1.7464	+7.3098%	+21.9544	+4.8846%	+4.8846%

Known prime factors (1 factor, 69.3 bits, 0.00241317% 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
2870587	712875134300218733983	21	69.272	124168878055293 3 × 31 × 79 × 16900623119	2020-08-30	79	16900623119	60.279	103.12	192.60

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%
2009-07-03T00:53:00	Carsten Kossendey	leela	15000	157500		-		-	-	0.003	-	-	0.718%
2010-12-22T11:37:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.272%
2011-01-03T22:20:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.376%
2011-01-21T23:30:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.544%
2011-02-05T01:49:00	markr	tiny	115000	2530000		-		-	-	0.028	-	-	2.684%
2016-09-15T03:47:42	Jocelyn Larouche	low 4M	153065	2783000	6	-		-	-	0.033	-	-	2.887%
2016-09-21T12:09:24	Jocelyn Larouche	low 4M	153065	3061300		-		-	-	0.035	-	-	2.951%
2016-12-18T19:43:10	Jocelyn Larouche	low 4M	183678	183678		-		-	-	0.021	-	-	1.182%
2017-01-10T10:25:08	Jocelyn Larouche	low 4M	220413	220413		-		-	-	0.025	-	-	1.297%
2017-03-11T20:25:02	Jocelyn Larouche	low 4M	317394	3173940	6	-		-	-	0.053	-	-	3.307%
2017-12-27T15:42:22	Jocelyn Larouche	low 4M	634788	6347880	6	-		-	-	0.106	-	-	4.185%
2019-10-26T17:50:08	masser	Manual testing	2880000	28800000	12	-		-	-	0.481	-	-	6.427%
2020-02-27T13:59:14	masser	Manual testing	5000000	200000000	12	-		-	-	1.750	-	-	9.179%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:23	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.054	-	-
2009-02-14T10:00:00	Sturle Sunde	letov.ifi	2⁶⁰	2⁶¹		-	-	0.054	-	-
2012-01-24T08:25:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.107	-	-
2013-01-10T10:24:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.342	-	-
2015-04-21T09:21:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.684	-	-
2015-04-21T09:21:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.302	-	-
2016-02-18T12:13:58	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.603	-	-
2017-11-12T17:07:19	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.206	-	-
2019-01-09T01:09:59	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.41	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.929 GHz-days
Estimated T-Level:	1.400

Digits	B1	Curves	Complete	FacMiss
20	11000	28 / 100	0.280	75.472%
25	50000	28 / 280	0.100	90.468%

New Calculation Method

Total ECM effort:	2.929 GHz-days
Estimated T-Level:	1.400

Digits	B1	Complete	FacMiss
20	11000	1.077	34.064%
25	50000	0.100	90.516%
30	250000	0.006	99.373%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		24	2.511
50000	5000000	712875134300218733983	4	0.418

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-03T22:24:00	Conductor	home	50000	5000000						3	0.314
2010-12-12T17:38:00	unconnected	X3220--xp	50000	5000000						3	0.314
2013-04-23T06:32:00	Donna Noble	PH2x6	50000	5000000						3	0.314
2015-07-14T03:20:00	Adel El-Atawy	MainMTV	50000	5000000						3	0.314
2015-07-14T04:37:00	Adel El-Atawy	MainMTV	50000	5000000						3	0.314
2019-06-03T09:58:26	Ondrej Vainlich	Intel_Corei5	50000	5000000						3	0.314
2020-08-04T04:37:53	Yxinity	Olga	50000	5000000						3	0.314
2020-08-11T17:54:42	GAN	LMS-01	50000	5000000						3	0.314
2020-08-30T06:48:25	rextherunt	ice	50000	5000000	712875134300218733983	69.272	4	2		4	0.418

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-23T00:00:00	ANONYMOUS	v4_computers	F32F6F64401ED076	0.222
2018-09-21T03:26:54	kkmrkkblmbrbk	old	F32F6F64401ED076	0.222

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-08-30T14:33:18

CrypticClue

cruncher

712875134300218733983

488CC9B80B262377

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 = 634788, B2 = 6347880 (P-1 stage 2)

B1 = 634788 (P-1 stage 1)

B1 = 317394, B2 = 3173940 (P-1 stage 2)

B1 = 317394 (P-1 stage 1)

B1 = 153065, B2 = 3061300 (P-1 stage 2)

B1 = 153065, B2 = 2783000 (P-1 stage 2)

B1 = 115000, B2 = 2530000 (P-1 stage 2)

B1 = 220413 (P-1 stage 1)

B1 = 183678 (P-1 stage 1)

B1 = 153065 (P-1 stage 1)

B1 = 115000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 157500 (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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-08-30T14:33:18+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