M2495501 Mersenne number exponent details

Residue

Status

L-L

DAFC1CDBE2D0AF22

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	11.9070	67.1642%	2382500	85770100	0.6965	8.2006%	12.6035	69.8569%	2.6927%
PrimeNet	2⁵⁹	0.0308	62.7119%	10000	180000	0.0019	2.5370%	0.0327	63.6579%	0.9460%
GPU72	2⁶³	0.6396	65.0794%	11000	160000	0.0019	1.3816%	0.6415	65.5618%	0.4825%
Difference	+4	+11.2674	+2.0848%	+2371500	+85610100	+0.6946	+6.8190%	+11.9621	+4.2951%	+4.2951%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

11.9070

67.1642%

2382500

85770100

0.6965

8.2006%

12.6035

69.8569%

2.6927%

PrimeNet

2⁵⁹

0.0308

62.7119%

10000

180000

0.0019

2.5370%

0.0327

63.6579%

0.9460%

GPU72

2⁶³

0.6396

65.0794%

11000

160000

0.0019

1.3816%

0.6415

65.5618%

0.4825%

Difference

+11.2674

+2.0848%

+2371500

+85610100

+0.6946

+6.8190%

+11.9621

+4.2951%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2495501	50730560908651688809617559	26	85.391	10164404043246564279 3² × 7 × 29 × 6337 × 50359 × 17433419	2014-12-08	50359	17433419	3,411,122	0.1003	0.1784

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2495501

50730560908651688809617559

85.391

10164404043246564279
3² × 7 × 29 × 6337 × 50359 × 17433419

2014-12-08

50359

17433419

3,411,122

0.1003

0.1784

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-23T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.291%
2003-10-31T00:00:00	Team Prime Rib	v4_computers	15000	228750		-		-	-	0.003	-	-	0.920%
2010-12-22T11:37:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.314%
2011-01-25T03:30:00	Oscar Östlin		95000	1971250		-		-	-	0.020	-	-	2.689%
2014-09-10T00:51:00	Jocelyn Larouche	Manual testing	120720	120720		-		-	-	0.012	-	-	1.054%
2014-12-08T01:09:00	mikr	MSI	2382500	85770100	12		50730560908651688809617559	26	85.391	0.697	0.346	1.393	8.201%
2019-07-04T12:37:58	alpertron	Manual testing	2000000	60000000	12	-	skipped known factor: 50730560908651688809617559	-	-	0.519	-	-	7.646%

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	-	-
2022-03-10T05:53:03	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.062	-	-
2009-01-11T09:19:00	Sturle Sunde	ginglo.ifi	2⁶⁰	2⁶¹		-	-	0.062	-	-
2012-06-11T12:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.123	-	-
2013-01-23T08:30:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.393	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.103 GHz-days
Estimated T-Level:	0.600

Digits	B1	Curves	Complete	FacMiss
20	11000	12 / 100	0.120	88.638%
25	50000	12 / 280	0.043	95.797%

New Calculation Method

Total ECM effort:	1.103 GHz-days
Estimated T-Level:	0.600

Digits	B1	Complete	FacMiss
20	11000	0.387	67.903%
25	50000	0.035	96.562%
30	250000	0.002	99.785%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.103

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-25T14:55:00	James Hintz	OMFG	50000	5000000						3	0.276
2010-04-02T05:11:00	James Classen	towerofart	50000	5000000						3	0.276
2012-07-11T20:19:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.276
2014-02-19T16:29:00	arnaud	srv-630	50000	5000000						3	0.276

date	userid	compid	res64	spent (GHz-days)
1999-08-16T00:00:00	ANONYMOUS	v4_computers	DAFC1CDBE2D0AF22	0.173

date

userid

compid

res64

spent (GHz-days)

1999-08-16T00:00:00

ANONYMOUS

v4_computers

DAFC1CDBE2D0AF22

0.173

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-14T23:41:38

kkmrkkblmbrbk

c4.xlarge

7D928F79FFC017__

2017-11-07T08:32:16

Oliver Kruse

GTX-2

50730560908651688809617559

7D928F79FFC017__

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 = 2382500, B2 = 85770100 (P-1 stage 2)

B1 = 2000000, B2 = 60000000 (P-1 stage 2)

B1 = 2382500 (P-1 stage 1)

B1 = 2000000 (P-1 stage 1)

B1 = 95000, B2 = 1971250 (P-1 stage 2)

B1 = 120720 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

B1 = 15000, B2 = 228750 (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

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