M2926487 Mersenne number exponent details

Residue

Status

L-L

6E7A0E5ED594C66A

double-checked

PRP

D33FE977143C455D

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	2⁶⁹	40.7953	68.1159%	1000000	20000000	0.2279	5.0509%	41.0232	69.7264%	1.6104%
PrimeNet	2⁵⁹	0.0262	62.7119%	13000	260000	0.0030	3.0693%	0.0292	63.8563%	1.1445%
GPU72	2⁶³	0.5454	65.0794%	17000	300000	0.0036	1.9447%	0.5490	65.7585%	0.6791%
Difference	+6	+40.2499	+3.0366%	+983000	+19700000	+0.2243	+3.1062%	+40.4742	+3.9679%	+3.9679%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

40.7953

68.1159%

1000000

20000000

0.2279

5.0509%

41.0232

69.7264%

1.6104%

PrimeNet

2⁵⁹

0.0262

62.7119%

13000

260000

0.0030

3.0693%

0.0292

63.8563%

1.1445%

GPU72

2⁶³

0.5454

65.0794%

17000

300000

0.0036

1.9447%

0.5490

65.7585%

0.6791%

Difference

+40.2499

+3.0366%

+983000

+19700000

+0.2243

+3.1062%

+40.4742

+3.9679%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2926487	21468600541451722164144439	26	84.150	3667981532371700637 3 × 15580393 × 78474304903	2021-06-02	15580393	78474304903	1,633,463	480.47	894.31

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2926487

21468600541451722164144439

84.150

3667981532371700637
3 × 15580393 × 78474304903

2021-06-02

15580393

78474304903

1,633,463

480.47

894.31

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	-	-	0.198%
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.120%
2010-11-12T15:15:00	markr	tiny	105000	2283750		-		-	-	0.025	-	-	2.294%
2015-04-27T09:55:00	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.228	-	-	5.051%

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		-	-	0.052	-	-
2009-02-14T16:37:00	Sturle Sunde	haydn.ifi	2⁶⁰	2⁶¹		-	-	0.052	-	-
2012-01-07T16:29:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.105	-	-
2013-01-07T13:49:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.335	-	-
2015-04-25T17:16:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.671	-	-
2015-04-25T17:16:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.277	-	-
2016-02-23T09:49:03	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.553	-	-
2017-11-22T00:30:13	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.107	-	-
2018-12-20T02:16:12	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.21	-	-
2021-05-31T09:33:00	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	20.43	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.871 GHz-days
Estimated T-Level:	3.750

Digits	B1	Curves	Complete	FacMiss
20	11000	75 / 100	0.750	47.059%
25	50000	75 / 280	0.268	76.465%

New Calculation Method

Total ECM effort:	7.871 GHz-days
Estimated T-Level:	3.750

Digits	B1	Complete	FacMiss
20	11000	2.419	8.898%
25	50000	0.219	80.360%
30	250000	0.013	98.663%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		74	7.766
50000	5000000	21468600541451722164144439	1	0.105

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-30T15:07:00	Richard Kint	Desktop	50000	5000000						3	0.315
2011-04-07T11:45:00	James Hintz	13_052010	50000	5000000						3	0.315
2013-06-13T19:57:00	Richard Kint	xps	50000	5000000						3	0.315
2015-12-26T18:08:21	Bruce	Desk7	50000	5000000						3	0.315
2017-05-23T04:41:12	driveByUpgrades	AMD8	50000	5000000						3	0.315
2019-08-10T07:36:44	Corey	Computer	50000	5000000						3	0.315
2020-08-27T11:30:53	daveward2005	Dave2	50000	5000000						7	0.735
2020-10-02T04:13:10	mnd9	kitchen	50000	5000000						7	0.735
2020-10-26T10:34:31	mnd9	221Lb	50000	5000000						7	0.735
2020-12-01T01:12:18	RIHATEC	i7-3770K	50000	5000000						7	0.735
2021-01-03T05:58:44	Zenzoma	AM3700X_1	50000	5000000						7	0.735
2021-02-03T16:48:45	arachnotron	Dell_i7	50000	5000000						7	0.735
2021-03-03T23:25:12	Zenzoma	AMD3970X	50000	5000000						7	0.735
2021-04-10T11:08:01	mnd9	50869	50000	5000000						7	0.735
2021-06-02T11:24:51	daveward2005	Dave2	50000	5000000	21468600541451722164144439	84.150	1	2	2884636981911287	1	0.105

date	userid	compid	res64	spent (GHz-days)
1999-05-02T00:00:00	ANONYMOUS	v4_computers	6E7A0E5ED594C66A	0.226
2018-10-06T10:46:52	kkmrkkblmbrbk	old	6E7A0E5ED594C66A	0.226

date

userid

compid

res64

spent (GHz-days)

1999-05-02T00:00:00

ANONYMOUS

v4_computers

6E7A0E5ED594C66A

0.226

2018-10-06T10:46:52

kkmrkkblmbrbk

old

6E7A0E5ED594C66A

0.226

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

B1 = 10000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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