M2126431 Mersenne number exponent details

Residue

Status

L-L

DBA9A9135317E63A

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	2⁶⁷	13.9736	67.1642%	500000	15000000	0.1230	5.1609%	14.0966	68.8588%	1.6946%
PrimeNet	2⁵⁸	0.0181	62.0690%	9000	160000	0.0016	2.6841%	0.0197	63.0871%	1.0181%
GPU72	2⁶²	0.2889	64.5161%	10000	140000	0.0016	1.4550%	0.2905	65.0324%	0.5163%
Difference	+5	+13.6847	+2.6481%	+490000	+14860000	+0.1214	+3.7059%	+13.8061	+3.8264%	+3.8264%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.9736

67.1642%

500000

15000000

0.1230

5.1609%

14.0966

68.8588%

1.6946%

PrimeNet

2⁵⁸

0.0181

62.0690%

9000

160000

0.0016

2.6841%

0.0197

63.0871%

1.0181%

GPU72

2⁶²

0.2889

64.5161%

10000

140000

0.0016

1.4550%

0.2905

65.0324%

0.5163%

Difference

+13.6847

+2.6481%

+490000

+14860000

+0.1214

+3.7059%

+13.8061

+3.8264%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2126431	991548348474326479217	21	69.748	233148488823368 2³ × 16987 × 1715639083	2008-12-17	16987	1715639083	104.44	8.9130	16.644

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2126431

991548348474326479217

69.748

233148488823368
2³ × 16987 × 1715639083

2008-12-17

16987

1715639083

104.44

8.9130

16.644

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-08-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.278%
2016-03-16T12:13:23	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.161%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

1999-01-29T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁸

0.018

-

-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.137 GHz-days
Estimated T-Level:	1.200

Digits	B1	Curves	Complete	FacMiss
20	11000	24 / 100	0.240	78.568%
25	50000	24 / 280	0.086	91.772%

New Calculation Method

Total ECM effort:	2.137 GHz-days
Estimated T-Level:	1.200

Digits	B1	Complete	FacMiss
20	11000	0.945	38.883%
25	50000	0.088	91.609%
30	250000	0.006	99.447%

ECM Summary

B1	B2	factor	curves	GHz-days
		991548348474326479217	1	0.00000e+0
50000	5000000		10	0.852
50000	5600000		7	0.626
50000	6264942		7	0.658

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-17T18:26:00	alan145	Bear4			991548348474326479217	69.748		1		1	-
2018-11-28T18:13:33	rucio		50000	5000000						3	0.256
2021-11-21T05:07:42	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.597
2022-04-07T22:34:35	Eric	miniPCWindows	50000	5600000						7	0.626
2022-06-26T04:22:41	MarkS	desktop-i7	50000	6264942						7	0.658

date	userid	compid	res64	spent (GHz-days)
1999-03-26T00:00:00	ANONYMOUS	v4_computers	DBA9A9135317E63A	0.140

date

userid

compid

res64

spent (GHz-days)

1999-03-26T00:00:00

ANONYMOUS

v4_computers

DBA9A9135317E63A

0.140

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-08T13:47:49

Oliver Kruse

GTX-1

991548348474326479217

77B7AB07148868__

2017-11-17T21:37:19

kkmrkkblmbrbk

c4.xlarge

991548348474326479217

77B7AB07148868__

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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