M2960161 Mersenne number exponent details

Residue

Status

L-L

9B301D27B46DE133

double-checked

PRP

22D51252DF979114

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	40.3312	68.1159%	1000000	20000000	0.2512	5.0576%	40.5823	69.7285%	1.6126%
PrimeNet	2⁶⁰	0.0519	63.3333%	12000	220000	0.0029	2.5089%	0.0548	64.2533%	0.9199%
GPU72	2⁶⁴	1.2024	65.6250%	12000	200000	0.0027	1.3476%	1.2052	66.0882%	0.4632%
Difference	+5	+39.1288	+2.4909%	+988000	+19800000	+0.2484	+3.7100%	+39.3772	+3.6403%	+3.6403%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

40.3312

68.1159%

1000000

20000000

0.2512

5.0576%

40.5823

69.7285%

1.6126%

PrimeNet

2⁶⁰

0.0519

63.3333%

12000

220000

0.0029

2.5089%

0.0548

64.2533%

0.9199%

GPU72

2⁶⁴

1.2024

65.6250%

12000

200000

0.0027

1.3476%

1.2052

66.0882%

0.4632%

Difference

+39.1288

+2.4909%

+988000

+19800000

+0.2484

+3.7100%

+39.3772

+3.6403%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2960161	17411618886872064207872543	26	83.848	2940991872886654511 19 × 163 × 949626048720263	2021-11-13	163	949626048720263	1,213,381	6,385,075	11,925,541

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2960161

17411618886872064207872543

83.848

2940991872886654511
19 × 163 × 949626048720263

2021-11-13

163

949626048720263

1,213,381

6,385,075

11,925,541

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		-		-	-	0.002	-	-	0.199%
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.120%
2010-10-31T16:35:00	markr	tiny	95000	1995000		-		-	-	0.024	-	-	2.179%
2015-05-08T13:54:00	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.251	-	-	5.058%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-05-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.052	-	-
2009-02-13T17:37:00	Sturle Sunde	bruch.ifi	2⁶⁰	2⁶¹		-	-	0.052	-	-
2011-12-09T02:39:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.104	-	-
2013-01-07T13:49:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.332	-	-
2015-04-29T14:58:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.663	-	-
2015-04-29T14:58:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.262	-	-
2016-02-26T10:03:34	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.524	-	-
2017-12-03T16:23:19	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.049	-	-
2018-12-24T05:50:47	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.10	-	-
2021-06-07T10:35:22	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	20.20	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	10.329 GHz-days
Estimated T-Level:	4.350

Digits	B1	Curves	Complete	FacMiss
20	11000	87 / 100	0.870	41.712%
25	50000	87 / 280	0.311	73.252%

New Calculation Method

Total ECM effort:	10.329 GHz-days
Estimated T-Level:	4.350

Digits	B1	Complete	FacMiss
20	11000	2.838	5.857%
25	50000	0.257	77.327%
30	250000	0.016	98.428%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		67	7.763
50000	5000000	17411618886872064207872543	6	0.695
50000	6750000		14	1.871

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-09T03:19:00	linded	imhotep	50000	5000000						3	0.348
2011-04-27T10:09:00	sannerud.com	Jim2010	50000	5000000						3	0.348
2013-07-15T03:47:00	Bruce	fx6840-21	50000	5000000						3	0.348
2016-01-04T16:06:58	Bruce	Desk7	50000	5000000						3	0.348
2017-06-13T11:44:53	alex	newwork	50000	5000000						3	0.348
2019-10-26T13:46:07	theSpirit83	i7-3632QM	50000	5000000						3	0.348
2020-09-15T13:12:28	daveward2005	Davy	50000	5000000						7	0.811
2020-10-15T23:37:44	lycorn	colab_DG_1	50000	5000000						7	0.811
2020-11-14T23:17:18	daveward2005	Dave2	50000	5000000						7	0.811
2020-12-23T07:10:34	mat10243x	K	50000	5000000						7	0.811
2021-01-23T15:20:54	nordi	sweet16	50000	6750000						7	0.935
2021-02-23T08:24:41	lycorn	colab_ES_1	50000	6750000						7	0.935
2021-03-29T00:27:28	daveward2005	Dave2	50000	5000000						7	0.811
2021-11-11T20:50:54	mnd9	50871b	50000	5000000						7	0.811
2021-11-12T05:17:48	daveward2005	Dave2	50000	5000000						7	0.811
2021-11-13T00:00:39	MarkS	desktop-i7	50000	5000000	17411618886872064207872543	83.848	6	2	3660193521628883	6	0.695

date	userid	compid	res64	spent (GHz-days)
1999-05-30T00:00:00	ANONYMOUS	v4_computers	9B301D27B46DE133	0.252
2018-10-14T11:53:44	kkmrkkblmbrbk	old	9B301D27B46DE133	0.252

date

userid

compid

res64

spent (GHz-days)

1999-05-30T00:00:00

ANONYMOUS

v4_computers

9B301D27B46DE133

0.252

2018-10-14T11:53:44

kkmrkkblmbrbk

old

9B301D27B46DE133

0.252

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 = 95000, B2 = 1995000 (P-1 stage 2)

B1 = 95000 (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

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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