M31029827 Mersenne number exponent details

Residue

Status

L-L

1BCB01B09FD6EE3F

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	30.8198	65.2778%	345000	4312500	0.8956	3.2389%	31.7154	66.4024%	1.1246%
PrimeNet	2⁶⁷	0.9576	62.6866%	140000	5000000	0.6460	4.9827%	1.6036	64.5458%	1.8592%
GPU72	2⁷¹	15.4071	64.7887%	220000	6500000	0.8972	3.6891%	16.3043	66.0877%	1.2990%
Difference	+1	+15.4128	+0.4890%	+125000	-2187500	-0.0016	-0.4502%	+15.4112	+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

30.8198

65.2778%

345000

4312500

0.8956

3.2389%

31.7154

66.4024%

1.1246%

PrimeNet

2⁶⁷

0.9576

62.6866%

140000

5000000

0.6460

4.9827%

1.6036

64.5458%

1.8592%

GPU72

2⁷¹

15.4071

64.7887%

220000

6500000

0.8972

3.6891%

16.3043

66.0877%

1.2990%

Difference

+15.4128

+0.4890%

+125000

-2187500

-0.0016

-0.4502%

+15.4112

+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
31029827	470297443489971420074041	24	78.638	7578151233166260 2² × 3² × 5 × 23² × 31 × 293 × 8762051	2021-09-23	529	8762051	2,587.7	0.7627	1.4230

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

31029827

470297443489971420074041

78.638

7578151233166260
2² × 3² × 5 × 23² × 31 × 293 × 8762051

2021-09-23

529

8762051

2,587.7

0.7627

1.4230

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
2021-09-23T05:38:30	ATH	5960X	300000	12300000	2	7	470297443489971420074041	P-1	24	78.638	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	ANONYMOUS	v4_computers	2¹	2⁶⁷		-	-	0.958	-	-
2011-05-24T20:23:00	Ungelovende	Manual testing	2⁶⁷	2⁶⁸		-	-	0.963	-	-
2012-05-08T09:41:00	bcp19	Manual testing	2⁶⁸	2⁶⁹		-	-	1.927	-	-
2013-03-27T20:45:00	bcp19	Manual testing	2⁶⁹	2⁷⁰		-	-	3.853	-	-
2019-01-01T21:16:14	ramgeis	Manual testing	2⁷⁰	2⁷¹		-	-	7.706	-	-
2019-06-25T10:18:08	LaurV	Manual testing	2⁷¹	2⁷²		-	-	15.41	-	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2006-02-01T00:00:00	ANONYMOUS	v4_computers	1BCB01B09FD6EE3F	34.15
2013-09-06T03:11:00	Lilith	Manual testing	73E931BA994BEA__	34.15
2013-12-27T21:52:00	forrest-lumpkin	ThinkCP_Opteron	1BCB01B09FD6EE3F	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 = 345000, B2 = 4312500 (P-1 stage 2)

B1 = 345000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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