M2906741 Mersenne number exponent details

Residue

Status

L-L

8517045C752E8B29

double-checked

PRP

584AC333BFDDE339

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	20.5057	67.6471%	5000000	200000000	1.7498	9.1900%	22.2555	70.6203%	2.9732%
PrimeNet	2⁵⁹	0.0264	62.7119%	13000	240000	0.0028	3.0034%	0.0293	63.8318%	1.1199%
GPU72	2⁶³	0.5491	65.0794%	16000	300000	0.0035	1.9098%	0.5526	65.7463%	0.6669%
Difference	+5	+19.9567	+2.5677%	+4984000	+199700000	+1.7463	+7.2802%	+21.7029	+4.8740%	+4.8740%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

20.5057

67.6471%

5000000

200000000

1.7498

9.1900%

22.2555

70.6203%

2.9732%

PrimeNet

2⁵⁹

0.0264

62.7119%

13000

240000

0.0028

3.0034%

0.0293

63.8318%

1.1199%

GPU72

2⁶³

0.5491

65.0794%

16000

300000

0.0035

1.9098%

0.5526

65.7463%

0.6669%

Difference

+19.9567

+2.5677%

+4984000

+199700000

+1.7463

+7.2802%

+21.7029

+4.8740%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2906741	21476551295474361899287	23	74.185	3694266413050623 3 × 521 × 2363574160621	2020-12-30	521	2363574160621	2,069.2	14,422	26,936

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2906741

21476551295474361899287

74.185

3694266413050623
3 × 521 × 2363574160621

2020-12-30

521

2363574160621

2,069.2

14,422

26,936

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-02T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.245%
2009-08-13T12:59:00	Carsten Kossendey	durandal	15000	168750		-		-	-	0.003	-	-	0.736%
2010-12-24T02:50:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.273%
2011-01-28T17:32:00	markr	tiny	105000	2283750		-		-	-	0.025	-	-	2.580%
2015-04-25T17:32:00	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.228	-	-	5.534%
2020-03-23T02:09:32	masser	Manual testing	5000000	200000000	12	-		-	-	1.750	-	-	9.190%

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	-	-
2009-02-14T18:44:00	Sturle Sunde	klughardt.ifi	2⁶⁰	2⁶¹		-	-	0.053	-	-
2011-12-12T11:46:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.106	-	-
2013-01-07T13:47:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.338	-	-
2015-04-25T17:15:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.675	-	-
2015-04-25T17:15:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.285	-	-
2016-02-22T09:35:50	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.571	-	-
2017-11-19T23:57:48	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.142	-	-
2018-12-17T01:16:49	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.28	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.822 GHz-days
Estimated T-Level:	2.300

Digits	B1	Curves	Complete	FacMiss
20	11000	46 / 100	0.460	62.982%
25	50000	46 / 280	0.164	84.825%

New Calculation Method

Total ECM effort:	4.822 GHz-days
Estimated T-Level:	2.300

Digits	B1	Complete	FacMiss
20	11000	1.484	22.676%
25	50000	0.134	87.449%
30	250000	0.008	99.178%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		42	4.403
50000	5000000	21476551295474361899287	4	0.419

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-13T17:44:00	Matt	Dell	50000	5000000						3	0.314
2011-03-22T02:42:00	Smurgs	Praca	50000	5000000						3	0.314
2013-05-24T10:23:00	Richard Kint	xps	50000	5000000						3	0.314
2015-12-22T10:55:38	Bruce	Desk7	50000	5000000						3	0.314
2016-09-18T02:33:28	Bruce	test	50000	5000000						3	0.314
2019-07-09T09:30:46	furkell	furkell1	50000	5000000						3	0.314
2020-08-14T10:16:07	mnd9	50871b	50000	5000000						3	0.314
2020-09-05T04:34:14	M. R. Mayer	nimbus	50000	5000000						7	0.734
2020-10-07T12:48:45	tottenhoff	4-of-4-Ryzen-5-3600	50000	5000000						7	0.734
2020-12-09T20:18:03	Zenzoma	AMD3970X	50000	5000000						7	0.734
2020-12-30T18:10:20	mnd9	kitchen	50000	5000000	21476551295474361899287	74.185	4	2	621379251392578	4	0.419

date	userid	compid	res64	spent (GHz-days)
1999-05-16T00:00:00	ANONYMOUS	v4_computers	8517045C752E8B29	0.225
2018-10-01T20:47:56	kkmrkkblmbrbk	old	8517045C752E8B29	0.225

date

userid

compid

res64

spent (GHz-days)

1999-05-16T00:00:00

ANONYMOUS

v4_computers

8517045C752E8B29

0.225

2018-10-01T20:47:56

kkmrkkblmbrbk

old

8517045C752E8B29

0.225

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, B2 = 168750 (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

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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