M31024991 Mersenne number exponent details

Residue

Status

L-L

5678BBCB4178932A

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁷²	30.8246	65.2778%	380000	10260000	1.4656	3.9472%	32.2902	66.6483%	1.3706%
PrimeNet	2⁶⁷	0.9577	62.6866%	140000	5000000	0.6460	4.9826%	1.6038	64.5458%	1.8592%
GPU72	2⁷¹	15.4095	64.7887%	220000	6500000	0.8972	3.6890%	16.3067	66.0877%	1.2989%
Difference	+1	+15.4152	+0.4890%	+160000	+3760000	+0.5684	+0.2582%	+15.9836	+0.5606%	+0.5606%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

30.8246

65.2778%

380000

10260000

1.4656

3.9472%

32.2902

66.6483%

1.3706%

PrimeNet

2⁶⁷

0.9577

62.6866%

140000

5000000

0.6460

4.9826%

1.6038

64.5458%

1.8592%

GPU72

2⁷¹

15.4095

64.7887%

220000

6500000

0.8972

3.6890%

16.3067

66.0877%

1.2989%

Difference

+15.4152

+0.4890%

+160000

+3760000

+0.5684

+0.2582%

+15.9836

+0.5606%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
31024991	62705258306328564713249	23	75.731	1010560459249264 2⁴ × 7 × 11 × 1187 × 691036321	2021-09-23	1187	691036321	378.18	60.091	112.23

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

31024991

62705258306328564713249

75.731

1010560459249264
2⁴ × 7 × 11 × 1187 × 691036321

2021-09-23

1187

691036321

378.18

60.091

112.23

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2006-01-01T00:00:00	Sturle Sunde	v4_computers	380000	10260000		-		-	-	1.466	-	-	3.947%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-09-23T15:31:55	ATH	ec2-P_1	300000	10800000	2	7	62705258306328564713249	P+1	23	75.731	1.675

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-08-31T00:00:00	Net_Force	v4_computers	2¹	2⁵⁶		-	-	0.000	-	-
2003-06-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.002	-	-
2005-09-03T00:00:00	Remote009	v4_computers	2¹	2⁶⁷		-	-	0.958	-	-
2011-05-24T20:23:00	Ungelovende	Manual testing	2⁶⁷	2⁶⁸		-	-	0.963	-	-
2012-05-08T12:43:00	bcp19	Manual testing	2⁶⁸	2⁶⁹		-	-	1.927	-	-
2013-03-27T08:46:00	bcp19	Manual testing	2⁶⁹	2⁷⁰		-	-	3.854	-	-
2018-11-19T12:11:00	ramgeis	Manual testing	2⁷⁰	2⁷¹		-	-	7.708	-	-
2019-06-24T22:18:08	LaurV	Manual testing	2⁷¹	2⁷²		-	-	15.42	-	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2009-05-11T10:06:00	DocPL	Gibson	5678BBCB4178932A	34.15
2013-10-15T04:30:00	GrunwalderGIMP	compute-0-4	5678BBCB4178932A	34.15

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 = 380000, B2 = 10260000 (P-1 stage 2)

B1 = 300000, B2 = 10800000 (P+1 stage 2)

B1 = 380000 (P-1 stage 1)

B1 = 300000 (P+1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁵⁹

2⁵⁶

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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