M31054391 Mersenne number exponent details

Residue

Status

L-L

B72D9CAD68C6D2A3

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	2⁷¹	15.3949	64.7887%	285000	1425000	0.5540	2.6612%	15.9489	65.7258%	0.9371%
PrimeNet	2⁶⁷	0.9568	62.6866%	140000	5000000	0.6460	4.9832%	1.6029	64.5460%	1.8594%
GPU72	2⁷¹	15.3949	64.7887%	220000	6500000	0.8972	3.6895%	16.2921	66.0878%	1.2991%
Difference	-	-	-	+65000	-5075000	-0.3432	-1.0282%	-0.3432	-0.3621%	-0.3621%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷¹

15.3949

64.7887%

285000

1425000

0.5540

2.6612%

15.9489

65.7258%

0.9371%

PrimeNet

2⁶⁷

0.9568

62.6866%

140000

5000000

0.6460

4.9832%

1.6029

64.5460%

1.8594%

GPU72

2⁷¹

15.3949

64.7887%

220000

6500000

0.8972

3.6895%

16.2921

66.0878%

1.2991%

Difference

+65000

-5075000

-0.3432

-1.0282%

-0.3432

-0.3621%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
31054391	138780880319602725872119	24	76.877	2234480790809949 3 × 11 × 11489 × 13883 × 424519	2021-10-03	13883	424519	820.18	0.0579	0.0689

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

31054391

138780880319602725872119

76.877

2234480790809949
3 × 11 × 11489 × 13883 × 424519

2021-10-03

13883

424519

820.18

0.0579

0.0689

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	285000	1425000		-	MISSED FACTOR!	-	-	0.554	-	-	2.661%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-10-03T00:55:27	ATH	5960X	300000	7200000	2	7	138780880319602725872119	P-1	24	76.877	1.245

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	ANONYMOUS	v4_computers	2¹	2⁶⁸		-	-	1.919	-	-
2012-05-21T11:58:00	apsen	Manual testing	2⁶⁸	2⁶⁹		-	-	1.925	-	-
2013-02-04T08:09:00	Architects Cubed	Manual testing	2⁶⁹	2⁷⁰		-	-	3.850	-	-
2018-04-22T20:57:28	ramgeis	Manual testing	2⁷⁰	2⁷¹		-	-	7.700	-	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2006-04-14T00:00:00	ANONYMOUS	v4_computers	B72D9CAD68C6D2A3	34.18
2013-03-08T10:30:00	GrunwalderGIMP	Lyc-i7	B72D9CAD68C6D2A3	34.18

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 = 7200000 (P-1 stage 2)

B1 = 285000, B2 = 1425000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 285000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

TF factor-bounds graph:

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

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