M2310551 Mersenne number exponent details

Residue

Status

L-L

FF2D231759E92DCC

double-checked

PRP

F4CC8FEC3C0BDA0D

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	51.6703	68.1159%	6000000	180000000	1.5164	8.2999%	53.1866	70.7623%	2.6463%
PrimeNet	2⁵⁸	0.0166	62.0690%	10000	190000	0.0019	2.9305%	0.0186	63.1805%	1.1116%
GPU72	2⁶²	0.2659	64.5161%	12000	200000	0.0022	1.7391%	0.2681	65.1332%	0.6171%
Difference	+7	+51.4044	+3.5998%	+5988000	+179800000	+1.5142	+6.5608%	+52.9185	+5.6290%	+5.6290%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

51.6703

68.1159%

6000000

180000000

1.5164

8.2999%

53.1866

70.7623%

2.6463%

PrimeNet

2⁵⁸

0.0166

62.0690%

10000

190000

0.0019

2.9305%

0.0186

63.1805%

1.1116%

GPU72

2⁶²

0.2659

64.5161%

12000

200000

0.0022

1.7391%

0.2681

65.1332%

0.6171%

Difference

+51.4044

+3.5998%

+5988000

+179800000

+1.5142

+6.5608%

+52.9185

+5.6290%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2310551	454298843821273218717724057	27	88.554	98309633464328036628 2² × 3 × 8192469455360669719	2021-08-01	4	8192469455360669719	27,764,489	4.372e+10	8.166e+10

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2310551

454298843821273218717724057

88.554

98309633464328036628
2² × 3 × 8192469455360669719

2021-08-01

8192469455360669719

27,764,489

4.372e+10

8.166e+10

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2003-09-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.185%
2010-02-15T08:06:00	Bud	annan	500000	10000000		-		-	-	0.100	-	-	3.959%
2018-01-20T10:22:57	Sid & Andy	Hand_In_The_Box	6000000	180000000	12	-		-	-	1.516	-	-	8.300%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2003-09-14T00:00:00

ANONYMOUS

v4_computers

2048

204800

0.001

-

-

0.185%

2010-02-15T08:06:00

Bud

annan

500000

10000000

0.100

-

-

3.959%

2018-01-20T10:22:57

Sid & Andy

Hand_In_The_Box

6000000

180000000

1.516

-

-

8.300%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-02-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.017	-	-
2016-02-23T16:29:11	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.050	-	-
2009-01-15T04:20:00	Sturle Sunde	bakeng.ifi	2⁶⁰	2⁶¹		-	-	0.066	-	-
2012-05-23T08:51:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.133	-	-
2013-12-06T02:47:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.425	-	-
2015-03-03T21:35:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.850	-	-
2015-03-03T21:35:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.617	-	-
2015-10-22T10:17:24	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.234	-	-
2017-05-31T02:32:35	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.468	-	-
2019-04-29T13:20:26	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.94	-	-
2021-07-12T19:28:27	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	25.87	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.306 GHz-days
Estimated T-Level:	22.786

Digits	B1	Curves	Complete	FacMiss
20	11000	156 / 100	1.560	20.849%
25	50000	156 / 280	0.557	57.227%

New Calculation Method

Total ECM effort:	14.306 GHz-days
Estimated T-Level:	22.786

Digits	B1	Complete	FacMiss
20	11000	5.089	0.616%
25	50000	0.459	63.167%
30	250000	0.028	97.213%
35	1000000	0.001	99.871%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	50000		7	0.365
50000	5000000		146	12.93
50000	6750000		7	0.710
50000	6750000	454298843821273218717724057	3	0.304

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-21T10:54:00	dachshund	Ann	50000	5000000						3	0.266
2010-01-14T04:15:00	SubPrime	abd0	50000	5000000						3	0.266
2011-11-29T23:45:00	S36049	Wolle5	50000	5000000						3	0.266
2013-10-04T04:28:00	Bruce	apandya-DESK11	50000	5000000						3	0.266
2015-06-26T02:18:00	dragon325	Falken-i7-920	50000	5000000						3	0.266
2016-01-16T01:15:20	Jason U	Server7	50000	5000000						3	0.266
2016-04-21T22:31:43	Bruce	Desk6	50000	5000000						3	0.266
2016-08-10T18:55:49	Bruce	Desk6	50000	5000000						3	0.266
2017-01-14T16:17:03	Bruce	Desk6	50000	5000000						3	0.266
2017-08-29T10:16:26	Bruce	Desk6	50000	5000000						3	0.266
2018-01-26T22:34:10	Bruce	Desk6	50000	5000000						3	0.266
2018-07-21T13:46:45	Bruce	Desk6	50000	5000000						3	0.266
2019-10-22T20:39:45	monsted	rootweiler	50000	5000000						3	0.266
2020-03-09T16:16:09	mnd9	50869b	50000	5000000						3	0.266
2020-03-17T05:52:58	mnd9	l2lounge	50000	5000000						3	0.266
2020-03-27T12:05:50	MarkS	laptop64	50000	5000000						3	0.266
2020-04-08T12:53:24	mnd9	221Rb	50000	5000000						3	0.266
2020-04-21T22:26:01	nordi	sweet16	50000	5000000						3	0.266
2020-04-29T16:36:28	mnd9	libproj	50000	5000000						3	0.266
2020-05-10T02:10:49	mnd9	colab	50000	5000000						3	0.266
2020-05-24T16:50:43	Leo Custodio	G1-PRIME96-01	50000	5000000						3	0.266
2020-06-12T09:01:15	MarkS	desktop-i7	50000	5000000						3	0.266
2020-06-28T01:24:42	nordi	sweet16	50000	5000000						3	0.266
2020-07-04T14:04:45	GAN	LMS-10	50000	5000000						3	0.266
2020-07-11T05:40:45	GAN	LMS-15	50000	5000000						3	0.266
2020-07-17T00:24:52	GAN	LMS-12	50000	5000000						3	0.266
2020-07-23T07:45:47	IanGlencross	glenx24	50000	5000000						3	0.266
2020-08-06T14:31:27	GAN	LMS-18	50000	5000000						3	0.266
2020-08-14T22:46:46	GAN	OSB-02	50000	5000000						3	0.266
2020-08-16T03:36:10	M. R. Mayer	nimbus	50000	5000000						3	0.266
2020-09-08T09:27:30	mnd9	kitchen	50000	5000000						7	0.620
2020-10-10T07:53:21	J.R. Allen	lapasus	50000	5000000						7	0.620
2020-11-06T22:33:32	Albrecht Heeffer	R7-3800X	50000	5000000						7	0.620
2020-12-12T22:11:57	Zenzoma	AMD3970X	50000	5000000						7	0.620
2021-01-14T15:07:21	daveward2005	Dave2	50000	5000000						7	0.620
2021-02-13T15:23:01	RIHATEC	i7-3770K	50000	5000000						7	0.620
2021-03-14T20:13:22	daveward2005	Davy	50000	5000000						7	0.620
2021-04-22T17:41:47	Zenzoma	AMD3970X	50000	5000000						7	0.620
2021-06-12T05:41:55	EICCEZP	spectre	50000	50000						7	0.365
2021-06-17T03:20:23	LaurV	Zero818	50000	6750000						7	0.710
2021-08-01T07:14:11	nordi	sweet16	50000	6750000	454298843821273218717724057	88.554	3	2	87487189318977	3	0.304

date	userid	compid	res64	spent (GHz-days)
1998-02-08T00:00:00	ANONYMOUS	v4_computers	FF2D231759E92DCC	0.156
1999-05-30T00:00:00	ANONYMOUS	v4_computers	FF2D231759E92DCC	0.156
2018-05-03T15:51:17	kkmrkkblmbrbk	old	FF2D231759E92DCC	0.156

date

userid

compid

res64

spent (GHz-days)

1998-02-08T00:00:00

ANONYMOUS

v4_computers

FF2D231759E92DCC

0.156

1999-05-30T00:00:00

ANONYMOUS

v4_computers

FF2D231759E92DCC

0.156

2018-05-03T15:51:17

kkmrkkblmbrbk

old

FF2D231759E92DCC

0.156

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