M2979311 Mersenne number exponent details

Residue

Status

L-L

73E64DA96CCF06A3

double-checked

PRP

165B2437E6199AB0

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	20.0063	67.6471%	1000000	20000000	0.2512	5.5499%	20.2574	69.4426%	1.7956%
PrimeNet	2⁶⁰	0.0516	63.3333%	12000	220000	0.0029	2.5119%	0.0544	64.2544%	0.9210%
GPU72	2⁶⁴	1.1947	65.6250%	13000	200000	0.0029	1.3850%	1.1975	66.1011%	0.4761%
Difference	+4	+18.8116	+2.0221%	+987000	+19800000	+0.2483	+4.1649%	+19.0599	+3.3415%	+3.3415%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

20.0063

67.6471%

1000000

20000000

0.2512

5.5499%

20.2574

69.4426%

1.7956%

PrimeNet

2⁶⁰

0.0516

63.3333%

12000

220000

0.0029

2.5119%

0.0544

64.2544%

0.9210%

GPU72

2⁶⁴

1.1947

65.6250%

13000

200000

0.0029

1.3850%

1.1975

66.1011%

0.4761%

Difference

+18.8116

+2.0221%

+987000

+19800000

+0.2483

+4.1649%

+19.0599

+3.3415%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2979311	102741035195974339709423	24	76.443	17242415309441401 19 × 80783 × 11233744013	2020-09-13	80783	11233744013	5,738.3	75.543	141.07

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2979311

102741035195974339709423

76.443

17242415309441401
19 × 80783 × 11233744013

2020-09-13

80783

11233744013

5,738.3

75.543

141.07

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%
2010-10-26T01:40:00	markr	tiny	95000	1995000		-		-	-	0.024	-	-	2.460%
2015-05-08T13:54:00	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.251	-	-	5.550%

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	-	-
2009-02-14T11:18:00	Sturle Sunde	iago.ifi	2⁶⁰	2⁶¹		-	-	0.052	-	-
2011-11-29T11:41:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.103	-	-
2013-01-07T13:51:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.329	-	-
2015-04-29T14:58:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.659	-	-
2015-04-29T14:58:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.254	-	-
2016-02-28T22:17:43	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.508	-	-
2017-12-03T16:23:25	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.016	-	-
2018-12-27T01:47:28	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.03	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.088 GHz-days
Estimated T-Level:	0.900

Digits	B1	Curves	Complete	FacMiss
20	11000	18 / 100	0.180	83.451%
25	50000	18 / 280	0.064	93.763%

New Calculation Method

Total ECM effort:	2.088 GHz-days
Estimated T-Level:	0.900

Digits	B1	Complete	FacMiss
20	11000	0.581	55.954%
25	50000	0.052	94.888%
30	250000	0.003	99.677%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	1.740
50000	5000000	102741035195974339709423	3	0.348

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-06T11:56:00	Lukasz Wrobel	LINUX_01	50000	5000000						3	0.348
2011-05-11T20:02:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.348
2013-07-30T02:54:00	Youcef L	breitner	50000	5000000						3	0.348
2016-01-10T12:49:27	Bruce	Desk10	50000	5000000						3	0.348
2017-07-06T03:17:18	Lelikoid	QH	50000	5000000						3	0.348
2020-09-13T17:42:41	GAN	OSB-02	50000	5000000	102741035195974339709423	76.443	3	2	2865776234229087	3	0.348

date	userid	compid	res64	spent (GHz-days)
1999-05-16T00:00:00	ANONYMOUS	v4_computers	73E64DA96CCF06A3	0.254
2018-10-19T17:07:52	kkmrkkblmbrbk	old	73E64DA96CCF06A3	0.254

date

userid

compid

res64

spent (GHz-days)

1999-05-16T00:00:00

ANONYMOUS

v4_computers

73E64DA96CCF06A3

0.254

2018-10-19T17:07:52

kkmrkkblmbrbk

old

73E64DA96CCF06A3

0.254

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)

10²

10³

10⁴

10⁵

10⁶

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