M31062257 Mersenne number exponent details

Residue

Status

L-L

A02E6E0BDFD13D05

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	30.7876	65.2778%	345000	4312500	0.8956	3.2394%	31.6833	66.4026%	1.1248%
PrimeNet	2⁶⁷	0.9566	62.6866%	140000	5000000	0.6460	4.9834%	1.6026	64.5460%	1.8595%
GPU72	2⁷¹	15.3910	64.7887%	220000	6500000	0.8972	3.6896%	16.2882	66.0879%	1.2992%
Difference	+1	+15.3967	+0.4890%	+125000	-2187500	-0.0016	-0.4502%	+15.3951	+0.3147%	+0.3147%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

30.7876

65.2778%

345000

4312500

0.8956

3.2394%

31.6833

66.4026%

1.1248%

PrimeNet

2⁶⁷

0.9566

62.6866%

140000

5000000

0.6460

4.9834%

1.6026

64.5460%

1.8595%

GPU72

2⁷¹

15.3910

64.7887%

220000

6500000

0.8972

3.6896%

16.2882

66.0879%

1.2992%

Difference

+15.3967

+0.4890%

+125000

-2187500

-0.0016

-0.4502%

+15.3951

+0.3147%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
31062257	14399060770921547807903	23	73.608	231777439271743 1327 × 21323 × 8191283	2021-10-03	21323	8191283	101.35	0.7444	1.3303

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

31062257

14399060770921547807903

73.608

231777439271743
1327 × 21323 × 8191283

2021-10-03

21323

8191283

101.35

0.7444

1.3303

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2006-01-15T00:00:00	ANONYMOUS	v4_computers	345000	4312500		-		-	-	0.896	-	-	3.239%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-10-03T19:39:41	ATH	ec2-P_1	300000	6300000	2	7	14399060770921547807903	P+1	23	73.608	1.279

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	-	-
2005-09-03T00:00:00	WileECoyote	v4_computers	2¹	2⁶⁷		-	-	0.957	-	-
2011-05-27T17:57:00	Ungelovende	Manual testing	2⁶⁷	2⁶⁸		-	-	0.962	-	-
2012-06-03T22:41:00	bcp19	Manual testing	2⁶⁸	2⁶⁹		-	-	1.925	-	-
2013-01-29T00:47:00	LaurV	Manual testing	2⁶⁹	2⁷⁰		-	-	3.849	-	-
2018-04-22T20:57:11	ramgeis	Manual testing	2⁷⁰	2⁷¹		-	-	7.698	-	-
2019-06-29T10:18:11	LaurV	Manual testing	2⁷¹	2⁷²		-	-	15.40	-	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2006-05-12T00:00:00	ANONYMOUS	v4_computers	A02E6E0BDFD13D05	34.19
2013-11-26T15:10:00	WR	wr9	A02E6E0BDFD13D05	34.19

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 = 300000, B2 = 6300000 (P+1 stage 2)

B1 = 345000, B2 = 4312500 (P-1 stage 2)

B1 = 345000 (P-1 stage 1)

B1 = 300000 (P+1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

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