M2862997 Mersenne number exponent details

≡

M2862997

<<<

>>>

is 2 ^2862997 - 1

has 861848 decimal digits

takes 0.221 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	C13426AA05797AEE	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	20.8190	67.6471%	2870000	28700000	0.4790	6.4197%	21.2981	69.7240%	2.0770%
PrimeNet	2⁵⁹	0.0268	62.7119%	13000	240000	0.0028	2.9953%	0.0297	63.8287%	1.1169%
GPU72	2⁶³	0.5575	65.0794%	16000	280000	0.0034	1.8687%	0.5609	65.7319%	0.6526%
Difference	+5	+20.2616	+2.5677%	+2854000	+28420000	+0.4756	+4.5511%	+20.7372	+3.9921%	+3.9921%

Known prime factors (1 factor, 75.8 bits, 0.00264618% 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
2862997	63976740362261560117391	23	75.760	11173036570115435 5 × 19 × 53 × 6907 × 321278963	2020-08-01	6907	321278963	4,463.2	1.9611	3.6614

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	-	-	0.244%
2009-07-03T00:47:00	Carsten Kossendey	leela	15000	157500		-		-	-	0.003	-	-	0.717%
2010-12-22T11:37:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.272%
2011-01-03T14:35:00	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%
2011-02-09T04:18:00	markr	tiny	115000	2415000		-		-	-	0.027	-	-	2.654%
2016-08-25T04:44:02	Jocelyn Larouche	low4M	156599	4830000	6	-		-	-	0.046	-	-	3.272%
2016-12-19T18:37:53	Jocelyn Larouche	low 4M	187918	187918		-		-	-	0.021	-	-	1.195%
2017-01-10T10:25:12	Jocelyn Larouche	low 4M	225501	225501		-		-	-	0.025	-	-	1.312%
2017-04-04T20:17:33	Jocelyn Larouche	low 4M	324721	3247210	6	-		-	-	0.054	-	-	3.333%
2018-08-27T00:20:23	Jocelyn Larouche	low 4M	858008	1716016	6	-		-	-	0.101	-	-	3.027%
2018-08-30T21:10:23	Jocelyn Larouche	low 4M	858008	2574024	6	-		-	-	0.107	-	-	3.417%
2019-10-24T13:09:25	masser	Manual testing	2870000	28700000	12	-		-	-	0.479	-	-	6.420%

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	-	-
2009-02-12T16:24:00	Sturle Sunde	gigotte.ifi	2⁶⁰	2⁶¹		-	-	0.054	-	-
2012-02-03T20:21:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.107	-	-
2013-01-07T13:46:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.343	-	-
2015-04-21T09:21:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.686	-	-
2015-04-21T09:21:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.305	-	-
2016-02-18T12:13:56	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.610	-	-
2017-11-12T17:07:16	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.220	-	-
2019-01-08T01:21:04	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.44	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.196 GHz-days
Estimated T-Level:	1.050

Digits	B1	Curves	Complete	FacMiss
20	11000	21 / 100	0.210	80.973%
25	50000	21 / 280	0.075	92.762%

New Calculation Method

Total ECM effort:	2.196 GHz-days
Estimated T-Level:	1.050

Digits	B1	Complete	FacMiss
20	11000	0.677	50.793%
25	50000	0.061	94.061%
30	250000	0.004	99.624%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		18	1.882
50000	5000000	63976740362261560117391	3	0.314

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-22T14:38:00	bayanne	bayanne_my03	50000	5000000						3	0.314
2010-12-01T20:53:00	Mistel		50000	5000000						3	0.314
2013-04-19T19:45:00	Donna Noble	PH2x6	50000	5000000						3	0.314
2015-07-03T07:05:00	Adel El-Atawy	MainMTV	50000	5000000						3	0.314
2015-07-03T08:17:00	Adel El-Atawy	MainMTV	50000	5000000						3	0.314
2019-05-19T10:28:38	Claude Portenier	Petit-Idiot	50000	5000000						3	0.314
2020-08-01T22:15:50	GAN	LMS-08	50000	5000000	63976740362261560117391	75.760	3	2	2352676033717745	3	0.314

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-09-22T00:00:00	ANONYMOUS	v4_computers	C13426AA05797AEE	0.221

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-08-02T04:28:35

CrypticClue

cruncher

63976740362261560117391

E851E4146E70E4EC

2020-08-02T17:35:37

LOBES

Manual testing

63976740362261560117391

E851E4146E70E4EC

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 = 2870000, B2 = 28700000 (P-1 stage 2)

B1 = 2870000 (P-1 stage 1)

B1 = 858008, B2 = 2574024 (P-1 stage 2)

B1 = 858008, B2 = 1716016 (P-1 stage 2)

B1 = 858008 (P-1 stage 1)

B1 = 324721, B2 = 3247210 (P-1 stage 2)

B1 = 156599, B2 = 4830000 (P-1 stage 2)

B1 = 324721 (P-1 stage 1)

B1 = 115000, B2 = 2415000 (P-1 stage 2)

B1 = 225501 (P-1 stage 1)

B1 = 187918 (P-1 stage 1)

B1 = 156599 (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)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-08-02T17:35:37+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