M2467961 Mersenne number exponent details

Residue

Status

L-L

BE92A6BB44997475

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	12.0399	67.1642%	2000000	60000000	0.5190	7.6371%	12.5588	69.6719%	2.5077%
PrimeNet	2⁵⁹	0.0311	62.7119%	10000	180000	0.0019	2.5317%	0.0331	63.6559%	0.9440%
GPU72	2⁶³	0.6467	65.0794%	10000	160000	0.0018	1.3354%	0.6485	65.5457%	0.4663%
Difference	+4	+11.3932	+2.0848%	+1990000	+59840000	+0.5171	+6.3017%	+11.9103	+4.1262%	+4.1262%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.0399

67.1642%

2000000

60000000

0.5190

7.6371%

12.5588

69.6719%

2.5077%

PrimeNet

2⁵⁹

0.0311

62.7119%

10000

180000

0.0019

2.5317%

0.0331

63.6559%

0.9440%

GPU72

2⁶³

0.6467

65.0794%

10000

160000

0.0018

1.3354%

0.6485

65.5457%

0.4663%

Difference

+11.3932

+2.0848%

+1990000

+59840000

+0.5171

+6.3017%

+11.9103

+4.1262%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2467961	3285384425112569425787759	25	81.442	665607038586219439 829 × 241337 × 3326897843	2015-07-14	241337	3326897843	351,301	18.253	34.048

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2467961

3285384425112569425787759

81.442

665607038586219439
829 × 241337 × 3326897843

2015-07-14

241337

3326897843

351,301

18.253

34.048

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.290%
2003-10-31T00:00:00	Team Prime Rib	v4_computers	15000	232500		-		-	-	0.003	-	-	0.922%
2010-11-19T22:14:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.313%
2010-11-27T12:43:00	Jocelyn Larouche	Manual testing	246796	246796		-		-	-	0.025	-	-	1.520%
2013-10-22T23:19:00	David Campeau	i5-2500k	590000	15930000		-		-	-	0.143	-	-	5.413%
2018-09-28T17:01:33	alpertron	Manual testing	2000000	60000000	12	-		-	-	0.519	-	-	7.637%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-05-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.031	-	-
2022-03-10T05:52:59	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.062	-	-
2009-01-14T00:18:00	Sturle Sunde	giacco.ifi	2⁶⁰	2⁶¹		-	-	0.062	-	-
2012-06-08T11:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.124	-	-
2013-02-21T00:57:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.398	-	-
2015-03-03T21:37:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.796	-	-
2015-03-03T21:37:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.514	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.193 GHz-days
Estimated T-Level:	0.650

Digits	B1	Curves	Complete	FacMiss
20	11000	13 / 100	0.130	87.752%
25	50000	13 / 280	0.046	95.455%

New Calculation Method

Total ECM effort:	1.193 GHz-days
Estimated T-Level:	0.650

Digits	B1	Complete	FacMiss
20	11000	0.419	65.747%
25	50000	0.038	96.281%
30	250000	0.002	99.767%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.101
50000	5000000	3285384425112569425787759	1	0.092

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-13T04:50:00	Lukasz Wrobel	UNIX_05	50000	5000000						3	0.275
2010-03-17T19:23:00	James Classen	towerofart	50000	5000000						3	0.275
2012-05-20T21:40:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.275
2014-01-26T04:40:00	Bruce	snowflake	50000	5000000						3	0.275
2015-07-14T01:55:00	guru	w6	50000	5000000	3285384425112569425787759	81.442	1	2		1	0.092

date	userid	compid	res64	spent (GHz-days)
1999-05-16T00:00:00	ANONYMOUS	v4_computers	BE92A6BB44997475	0.171

date

userid

compid

res64

spent (GHz-days)

1999-05-16T00:00:00

ANONYMOUS

v4_computers

BE92A6BB44997475

0.171

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-14T10:11:54

kkmrkkblmbrbk

c4.xlarge

858EE978C43CF9__

2017-11-05T13:18:59

Oliver Kruse

GTX-3

3285384425112569425787759

858EE978C43CF9__

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 = 2000000, B2 = 60000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 590000, B2 = 15930000 (P-1 stage 2)

B1 = 590000 (P-1 stage 1)

B1 = 246796 (P-1 stage 1)

B1 = 15000, B2 = 232500 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

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