M31028317 Mersenne number exponent details

Residue

Status

L-L

F96679FCE63B5451

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	30.8213	65.2778%	165000	3135000	0.5216	2.6986%	31.3429	66.2148%	0.9370%
PrimeNet	2⁶⁷	0.9576	62.6866%	140000	5000000	0.6460	4.9827%	1.6037	64.5458%	1.8592%
GPU72	2⁷¹	15.4078	64.7887%	220000	6500000	0.8972	3.6891%	16.3050	66.0877%	1.2990%
Difference	+1	+15.4135	+0.4890%	-55000	-3365000	-0.3756	-0.9904%	+15.0379	+0.1271%	+0.1271%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

30.8213

65.2778%

165000

3135000

0.5216

2.6986%

31.3429

66.2148%

0.9370%

PrimeNet

2⁶⁷

0.9576

62.6866%

140000

5000000

0.6460

4.9827%

1.6037

64.5458%

1.8592%

GPU72

2⁷¹

15.4078

64.7887%

220000

6500000

0.8972

3.6891%

16.3050

66.0877%

1.2990%

Difference

+15.4135

+0.4890%

-55000

-3365000

-0.3756

-0.9904%

+15.0379

+0.1271%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
31028317	39892990219914408179311	23	75.079	642848115479715 3² × 5 × 139 × 13381 × 7680553	2021-09-21	13381	7680553	295.45	0.6881	1.2474

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

31028317

39892990219914408179311

75.079

642848115479715
3² × 5 × 139 × 13381 × 7680553

2021-09-21

13381

7680553

295.45

0.6881

1.2474

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-05-29T22:39:00	Carsten Kossendey	leela	165000	3135000		-		-	-	0.522	-	-	2.699%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-09-21T18:33:42	ATH	5960X	300000	12300000	2	7	39892990219914408179311	P-1	23	75.079	1.657

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	Team Prime Rib	v4_computers	2¹	2⁶⁸		-	-	1.921	-	-
2012-04-17T21:04:00	Stef42	Manual testing	2⁶⁸	2⁶⁹		-	-	1.927	-	-
2013-01-26T19:39:00	Chuck	Manual testing	2⁶⁹	2⁷⁰		-	-	3.853	-	-
2018-12-24T16:29:48	ramgeis	Manual testing	2⁷⁰	2⁷¹		-	-	7.707	-	-
2019-06-23T20:18:07	LaurV	Manual testing	2⁷¹	2⁷²		-	-	15.41	-	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2006-07-10T00:00:00	Grey Smith	v4_computers	F96679FCE63B5451	34.15
2013-04-12T10:27:00	HardyP Germany	ws-HP-Z800_3.6GHz	F96679FCE63B5451	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 = 300000, B2 = 12300000 (P-1 stage 2)

B1 = 165000, B2 = 3135000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 165000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁷²

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