M2932679 Mersenne number exponent details

Residue

Status

L-L

70F15F96D48116E1

double-checked

PRP

EE614B4B42F4E7EC

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	20.3244	67.6471%	1000000	20000000	0.2512	5.5400%	20.5755	69.4394%	1.7924%
PrimeNet	2⁵⁹	0.0262	62.7119%	13000	260000	0.0033	3.0704%	0.0295	63.8568%	1.1449%
GPU72	2⁶³	0.5442	65.0794%	17000	300000	0.0040	1.9455%	0.5482	65.7587%	0.6794%
Difference	+5	+19.7802	+2.5677%	+983000	+19700000	+0.2472	+3.5945%	+20.0273	+3.6807%	+3.6807%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

20.3244

67.6471%

1000000

20000000

0.2512

5.5400%

20.5755

69.4394%

1.7924%

PrimeNet

2⁵⁹

0.0262

62.7119%

13000

260000

0.0033

3.0704%

0.0295

63.8568%

1.1449%

GPU72

2⁶³

0.5442

65.0794%

17000

300000

0.0040

1.9455%

0.5482

65.7587%

0.6794%

Difference

+19.7802

+2.5677%

+983000

+19700000

+0.2472

+3.5945%

+20.0273

+3.6807%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2932679	1600543376706993832151	22	70.439	272880764772925 5² × 17 × 571 × 1124470031	2020-10-05	571	1124470031	97.804	7.5608	14.121

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2932679

1600543376706993832151

70.439

272880764772925
5² × 17 × 571 × 1124470031

2020-10-05

571

1124470031

97.804

7.5608

14.121

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	-	-	0.246%
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.145%
2010-11-09T16:44:00	markr	tiny	105000	2283750		-		-	-	0.028	-	-	2.584%
2015-04-29T15:00:00	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.251	-	-	5.540%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-04-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.026	-	-
2016-02-23T16:29:24	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.026	-	-
2009-02-13T05:23:00	Sturle Sunde	golli.ifi	2⁶⁰	2⁶¹		-	-	0.052	-	-
2011-12-19T07:19:00	Sebastian Hornbostel	Manual testing	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		-	-	0.669	-	-
2015-04-25T17:16:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.274	-	-
2016-02-23T09:49:05	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.548	-	-
2017-11-23T20:18:51	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.096	-	-
2018-12-20T02:16:15	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.19	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.239 GHz-days
Estimated T-Level:	1.400

Digits	B1	Curves	Complete	FacMiss
20	11000	28 / 100	0.280	75.472%
25	50000	28 / 280	0.100	90.468%

New Calculation Method

Total ECM effort:	3.239 GHz-days
Estimated T-Level:	1.400

Digits	B1	Complete	FacMiss
20	11000	0.903	40.526%
25	50000	0.082	92.161%
30	250000	0.005	99.499%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		25	2.892
50000	5000000	1600543376706993832151	3	0.347

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-05T14:55:00	Aca Arsov	backo6400	50000	5000000						3	0.347
2011-04-10T06:07:00	FJCrodericck	CenterServ	50000	5000000						3	0.347
2013-06-19T22:27:00	Bruce	fx6840-21	50000	5000000						3	0.347
2015-12-28T09:47:23	Bruce	Desk7	50000	5000000						3	0.347
2017-05-26T22:28:54	alex	newwork	50000	5000000						3	0.347
2019-08-25T20:35:59	Corey	Computer	50000	5000000						3	0.347
2020-09-01T21:40:18	IanGlencross	glenx24	50000	5000000						7	0.810
2020-10-05T13:27:51	daveward2005	Dave2	50000	5000000	1600543376706993832151	70.439	3	2	335593094994622	3	0.347

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-05-16T00:00:00	ANONYMOUS	v4_computers	70F15F96D48116E1	0.250
1999-05-09T00:00:00	ANONYMOUS	v4_computers	70F15F96D48116E1	0.250
2018-10-08T08:47:34	kkmrkkblmbrbk	old	70F15F96D48116E1	0.250

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)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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