M2916931 Mersenne number exponent details

is 2 ^2916931 - 1

has 878084 decimal digits

takes 0.225 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	20.4341	67.6471%	5000000	200000000	1.7498	9.1929%	22.1839	70.6212%	2.9742%
PrimeNet	2⁵⁹	0.0263	62.7119%	13000	260000	0.0030	3.0675%	0.0293	63.8557%	1.1438%
GPU72	2⁶³	0.5472	65.0794%	16000	300000	0.0035	1.9111%	0.5507	65.7467%	0.6674%
Difference	+5	+19.8869	+2.5677%	+4984000	+199700000	+1.7463	+7.2819%	+21.6332	+4.8745%	+4.8745%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2916931	227858338073460947417109463	27	87.558	39057889623282303801 3 × 617 × 887 × 23789139618173	2021-04-02	887	23789139618173	18,329,599	145,153	271,106

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-13T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.246%
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.145%
2010-11-13T11:54:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.002	-	-	0.213%
2010-11-15T22:33:00	markr	tiny	105000	2283750		-		-	-	0.025	-	-	2.582%
2015-04-25T17:20:00	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.228	-	-	5.537%
2020-04-01T21:20:18	masser	Manual testing	5000000	200000000	12	-		-	-	1.750	-	-	9.193%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:24	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.053	-	-
2009-02-14T00:12:00	Sturle Sunde	krebs.ifi	2⁶⁰	2⁶¹		-	-	0.053	-	-
2011-12-22T17:30:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.105	-	-
2013-01-10T21:10:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.337	-	-
2015-04-25T17:15:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.673	-	-
2015-04-25T17:15:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.281	-	-
2016-02-17T03:24:02	Yxinity	Manual testing	2⁶⁵	2⁶⁶		-	-	2.562	-	-
2017-11-19T23:57:51	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.124	-	-
2018-12-18T01:52:41	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.25	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.132 GHz-days
Estimated T-Level:	3.400

Digits	B1	Curves	Complete	FacMiss
20	11000	68 / 100	0.680	50.489%
25	50000	68 / 280	0.243	78.404%

New Calculation Method

Total ECM effort:	7.132 GHz-days
Estimated T-Level:	3.400

Digits	B1	Complete	FacMiss
20	11000	2.615	7.314%
25	50000	0.242	78.506%
30	250000	0.015	98.485%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		67	7.027
50000	5000000	227858338073460947417109463	1	0.105

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-31T06:17:00	mdrg	MDRG02	50000	5000000						3	0.315
2011-03-29T15:21:00	S00030	op9020-usff	50000	5000000						3	0.315
2013-06-07T05:51:00	Smurgs	Praca	50000	5000000						3	0.315
2015-12-24T15:09:16	Bruce	Desk7	50000	5000000						3	0.315
2016-09-19T09:41:36	Bruce	test	50000	5000000						3	0.315
2019-07-24T07:38:34	Claude Portenier	Petit-Idiot	50000	5000000						3	0.315
2020-08-21T23:13:13	GAN	KL-SCH02	50000	5000000						7	0.734
2020-09-25T14:13:01	LaurV	debilis	50000	5000000						7	0.734
2020-10-19T06:41:13	nordi	sweet16	50000	5000000						7	0.734
2020-11-21T19:05:47	RIHATEC	i7-3770K	50000	5000000						7	0.734
2020-12-28T22:33:50	daveward2005	Dave2	50000	5000000						7	0.734
2021-01-07T02:47:34	Cork	Manual testing	50000	5000000						7	0.734
2021-02-26T21:47:19	Zenzoma	AMD3970X	50000	5000000						7	0.734
2021-04-02T12:03:23	Zenzoma	AMD3970X	50000	5000000	227858338073460947417109463	87.558	1	2	2307852215159787	1	0.105

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-16T00:00:00	ANONYMOUS	v4_computers	231AEC1C4F3184C1	0.225
2018-10-04T11:59:34	kkmrkkblmbrbk	old	231AEC1C4F3184C1	0.225

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-04-03T12:36:11

Kirill Frolov

shodan1

227858338073460947417109463

378C6E42F5695CDD

2021-04-04T12:29:34

daveward2005

Davy

227858338073460947417109463

378C6E42F5695CDD

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 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 105000, B2 = 2283750 (P-1 stage 2)

B1 = 105000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

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

B1 = 10000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-04-04T12:29:34+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