M8117831 Mersenne number exponent details

Residue

Status

L-L

4E07E831F994BB9C

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	2⁶⁸	7.3425	66.1765%	215000	5375000	0.1878	4.0541%	7.5303	67.5477%	1.3712%
PrimeNet	2⁶³	0.1966	63.4921%	36000	900000	0.0315	3.6141%	0.2281	64.8115%	1.3194%
GPU72	2⁶⁷	3.6603	65.6716%	55000	1200000	0.0444	2.5728%	3.7048	66.5548%	0.8832%
Difference	+1	+3.6821	+0.5048%	+160000	+4175000	+0.1434	+1.4813%	+3.8255	+0.9929%	+0.9929%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

7.3425

66.1765%

215000

5375000

0.1878

4.0541%

7.5303

67.5477%

1.3712%

PrimeNet

2⁶³

0.1966

63.4921%

36000

900000

0.0315

3.6141%

0.2281

64.8115%

1.3194%

GPU72

2⁶⁷

3.6603

65.6716%

55000

1200000

0.0444

2.5728%

3.7048

66.5548%

0.8832%

Difference

+3.6821

+0.5048%

+160000

+4175000

+0.1434

+1.4813%

+3.8255

+0.9929%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
8117831	13640797413539394359	20	63.565	840175005709 13 × 29 × 31 × 97 × 741131	2012-09-22	97	741131	0.4002	0.0153	0.0286

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

8117831

13640797413539394359

63.565

840175005709
13 × 29 × 31 × 97 × 741131

2012-09-22

741131

0.4002

0.0153

0.0286

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-08-17T00:00:00	ANONYMOUS	v4_computers	35000	201250		-		-	-	0.017	-	-	1.224%
unknown			215000	5375000		-	MISSED FACTOR!	-	-	0.188	-	-	4.054%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-08-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.038	-	-
1998-09-13T00:00:00	Baquara	v4_computers	2¹	2⁶²		-	-	0.076	-	-
1999-03-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.197	-	-
2022-04-09T01:54:27	LordJulius	Manual testing	2¹	2⁶⁴	13640797413539394359	63.565	20	0.400	4.313	0.814
2022-04-09T01:54:27	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	0.460	-	-
2022-04-09T01:54:27	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	0.921	-	-
2022-04-09T01:54:27	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	1.841	-	-
2022-03-04T22:50:21	Flaukrotist	Manual testing	2⁶⁷	2⁶⁸		-	-	3.682	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:

0.000 GHz-days

Digits	B1	Curves	Complete	FacMiss

New Calculation Method

Total ECM effort:

0.000 GHz-days

Digits	B1	Complete	FacMiss

ECM Summary

B1	B2	factor	curves	GHz-days
		13640797413539394359	1	0.00000e+0

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2012-09-22T14:52:00	James Heinrich	Manual testing			13640797413539394359	63.565		1		1	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-09-30T00:00:00	ANONYMOUS	v4_computers	4E07E831F994BB9C	2.120
2003-04-27T00:00:00	Team Prime Rib	v4_computers	4E07E831F994BB9C	2.120

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-08-19T03:52:20

Oliver Kruse

GTX-5

13640797413539394359

2A514D8F81DE82__

2020-02-10T21:05:10

oodaira

com1

13640797413539394359

2A514D8F81DE82F5

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 = 215000, B2 = 5375000 (P-1 stage 2)

B1 = 215000 (P-1 stage 1)

B1 = 35000, B2 = 201250 (P-1 stage 2)

B1 = 35000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

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