M2131373 Mersenne number exponent details

Residue

Status

L-L

32129BAB39E581D4

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	13.9412	67.1642%	500000	15000000	0.1230	5.1624%	14.0642	68.8593%	1.6951%
PrimeNet	2⁵⁸	0.0180	62.0690%	9000	170000	0.0017	2.7293%	0.0197	63.1042%	1.0352%
GPU72	2⁶²	0.2882	64.5161%	10000	150000	0.0017	1.4863%	0.2899	65.0435%	0.5274%
Difference	+5	+13.6530	+2.6481%	+490000	+14850000	+0.1213	+3.6761%	+13.7743	+3.8158%	+3.8158%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.9412

67.1642%

500000

15000000

0.1230

5.1624%

14.0642

68.8593%

1.6951%

PrimeNet

2⁵⁸

0.0180

62.0690%

9000

170000

0.0017

2.7293%

0.0197

63.1042%

1.0352%

GPU72

2⁶²

0.2882

64.5161%

10000

150000

0.0017

1.4863%

0.2899

65.0435%

0.5274%

Difference

+13.6530

+2.6481%

+490000

+14850000

+0.1213

+3.6761%

+13.7743

+3.8158%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2131373	125739420907411894461630929	27	86.701	29497282011973477768 2³ × 11 × 103 × 503 × 2281 × 2836408859	2015-08-11	2281	2836408859	10,643,993	14.733	27.517

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2131373

125739420907411894461630929

86.701

29497282011973477768
2³ × 11 × 103 × 503 × 2281 × 2836408859

2015-08-11

2281

2836408859

10,643,993

14.733

27.517

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-01-12T23:59:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.598%
2011-01-22T08:38:00	James Heinrich	i7-920	140000	3045000		-		-	-	0.028	-	-	3.113%
2016-03-19T15:01:45	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.162%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-11-12T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.009	-	-
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2022-03-09T10:02:00	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.072	-	-
2009-01-05T05:33:00	Sturle Sunde	celair.ifi	2⁶⁰	2⁶¹		-	-	0.072	-	-
2012-04-14T21:49:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.144	-	-
2013-09-07T11:35:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.461	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.921	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.753	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.535 GHz-days
Estimated T-Level:	0.900

Digits	B1	Curves	Complete	FacMiss
20	11000	18 / 100	0.180	83.451%
25	50000	18 / 280	0.064	93.763%

New Calculation Method

Total ECM effort:	1.535 GHz-days
Estimated T-Level:	0.900

Digits	B1	Complete	FacMiss
20	11000	0.581	55.954%
25	50000	0.052	94.888%
30	250000	0.003	99.677%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	1.279
50000	5000000	125739420907411894461630929	3	0.256

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-05T20:27:00	tbw1h	tbw1h03	50000	5000000						3	0.256
2009-11-20T22:54:00	SubPrime	abd0	50000	5000000						3	0.256
2011-07-25T14:56:00	S36049	Wolle5	50000	5000000						3	0.256
2013-04-19T06:07:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.256
2014-12-04T15:08:00	AdolfNor	PC4	50000	5000000						3	0.256
2015-08-11T16:17:00	guru	w1	50000	5000000	125739420907411894461630929	86.701	3	2		3	0.256

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-11-12T00:00:00	ANONYMOUS	v4_computers	32129BAB39E581D4	0.140
1999-02-21T00:00:00	ANONYMOUS	v4_computers	32129BAB39E581D4	0.140

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-08T15:24:53

Oliver Kruse

GTX-1

125739420907411894461630929

B5CAE4CC6DAEB8__

2017-11-18T01:40:38

kkmrkkblmbrbk

c4.xlarge

125739420907411894461630929

B5CAE4CC6DAEB8__

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 = 140000, B2 = 3045000 (P-1 stage 2)

B1 = 140000 (P-1 stage 1)

B1 = 50000 (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