M2956741 Mersenne number exponent details

Residue

Status

L-L

2F6B4D6626329ABF

double-checked

PRP

3886035DA6046D__

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	20.1590	67.6471%	1000000	20000000	0.2512	5.5452%	20.4101	69.4411%	1.7940%
PrimeNet	2⁶⁰	0.0519	63.3333%	12000	220000	0.0029	2.5084%	0.0548	64.2531%	0.9197%
GPU72	2⁶⁴	1.2038	65.6250%	12000	200000	0.0027	1.3473%	1.2065	66.0881%	0.4631%
Difference	+4	+18.9552	+2.0221%	+988000	+19800000	+0.2484	+4.1979%	+19.2036	+3.3530%	+3.3530%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

20.1590

67.6471%

1000000

20000000

0.2512

5.5452%

20.4101

69.4411%

1.7940%

PrimeNet

2⁶⁰

0.0519

63.3333%

12000

220000

0.0029

2.5084%

0.0548

64.2531%

0.9197%

GPU72

2⁶⁴

1.2038

65.6250%

12000

200000

0.0027

1.3473%

1.2065

66.0881%

0.4631%

Difference

+18.9552

+2.0221%

+988000

+19800000

+0.2484

+4.1979%

+19.2036

+3.3530%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2956741	52291339196465729891159	23	75.469	8842732453817519 179 × 49400739965461	2020-12-23	179	49400739965461	2,990.7	332,160	620,382

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2956741

52291339196465729891159

75.469

8842732453817519
179 × 49400739965461

2020-12-23

179

49400739965461

2,990.7

332,160

620,382

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	-	-	0.247%
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.146%
2010-11-01T13:21:00	markr	tiny	95000	1995000		-		-	-	0.024	-	-	2.457%
2015-05-02T08:23:00	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.251	-	-	5.545%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-04-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.026	-	-
1999-05-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.052	-	-
2009-02-13T20:17:00	Sturle Sunde	graun.ifi	2⁶⁰	2⁶¹		-	-	0.052	-	-
2011-12-12T10:50:00	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		-	-	0.664	-	-
2015-04-29T14:58:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.264	-	-
2016-02-26T10:03:33	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.527	-	-
2017-11-28T10:01:37	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.055	-	-
2018-12-24T00:53:34	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.11	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.981 GHz-days
Estimated T-Level:	2.150

Digits	B1	Curves	Complete	FacMiss
20	11000	43 / 100	0.430	64.910%
25	50000	43 / 280	0.154	85.740%

New Calculation Method

Total ECM effort:	4.981 GHz-days
Estimated T-Level:	2.150

Digits	B1	Complete	FacMiss
20	11000	1.654	19.131%
25	50000	0.153	85.811%
30	250000	0.010	99.039%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		39	4.518
50000	5000000	52291339196465729891159	4	0.463

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-02T20:07:00	Anu Järvi	Anu	50000	5000000						3	0.348
2011-04-25T08:38:00	sannerud.com	Jens2010	50000	5000000						3	0.348
2013-07-11T03:15:00	Bruce	fx6840-21	50000	5000000						3	0.348
2016-01-03T20:58:15	Bruce	Desk7	50000	5000000						3	0.348
2017-06-20T12:20:03	Lelikoid	QH	50000	5000000						3	0.348
2019-10-21T05:57:26	theSpirit83	i7-3632QM	50000	5000000						3	0.348
2020-09-14T10:04:31	MarkS	desktop-i7	50000	5000000						7	0.811
2020-10-15T04:42:44	IanGlencross	glenx24	50000	5000000						7	0.811
2020-11-14T20:47:40	lycorn	colab_A	50000	5000000						7	0.811
2020-12-23T06:25:01	rextherunt	ice	50000	5000000	52291339196465729891159	75.469	4	2		4	0.463

date	userid	compid	res64	spent (GHz-days)
1999-08-22T00:00:00	ANONYMOUS	v4_computers	2F6B4D6626329ABF	0.252
2018-10-13T19:31:20	kkmrkkblmbrbk	old	2F6B4D6626329ABF	0.252

date

userid

compid

res64

spent (GHz-days)

1999-08-22T00:00:00

ANONYMOUS

v4_computers

2F6B4D6626329ABF

0.252

2018-10-13T19:31:20

kkmrkkblmbrbk

old

2F6B4D6626329ABF

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

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