M2475163 Mersenne number exponent details

Residue

Status

L-L

B9D69246221B664C

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	12.0048	67.1642%	2000000	60000000	0.5190	7.6394%	12.5238	69.6726%	2.5085%
PrimeNet	2⁵⁹	0.0310	62.7119%	10000	180000	0.0019	2.5331%	0.0330	63.6564%	0.9446%
GPU72	2⁶³	0.6448	65.0794%	11000	160000	0.0019	1.3793%	0.6467	65.5610%	0.4817%
Difference	+4	+11.3600	+2.0848%	+1989000	+59840000	+0.5170	+6.2601%	+11.8771	+4.1116%	+4.1116%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.0048

67.1642%

2000000

60000000

0.5190

7.6394%

12.5238

69.6726%

2.5085%

PrimeNet

2⁵⁹

0.0310

62.7119%

10000

180000

0.0019

2.5331%

0.0330

63.6564%

0.9446%

GPU72

2⁶³

0.6448

65.0794%

11000

160000

0.0019

1.3793%

0.6467

65.5610%

0.4817%

Difference

+11.3600

+2.0848%

+1989000

+59840000

+0.5170

+6.2601%

+11.8771

+4.1116%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2475163	111793594203498544935497	24	76.565	22583077196026796 2² × 32643887 × 172950277	2018-07-16	32643887	172950277	12,040	4.0519	6.6817

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2475163

111793594203498544935497

76.565

22583077196026796
2² × 32643887 × 172950277

2018-07-16

32643887

172950277

12,040

4.0519

6.6817

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	228750		-		-	-	0.003	-	-	0.918%
2010-11-20T12:24:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.313%
2010-12-11T00:04:00	Jocelyn Larouche	Manual testing	247516	247516		-		-	-	0.025	-	-	1.523%
2013-10-30T11:47:00	David Campeau	i5-2500k	595000	16065000		-		-	-	0.145	-	-	5.429%
2018-09-28T16:27:07	alpertron	Manual testing	2000000	60000000	12	-		-	-	0.519	-	-	7.639%

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	-	-
2016-02-23T16:29:15	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.031	-	-
2009-01-15T03:16:00	Sturle Sunde	gouffy.ifi	2⁶⁰	2⁶¹		-	-	0.062	-	-
2012-06-08T20:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.124	-	-
2013-02-21T00:57:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.397	-	-
2015-03-03T21:37:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.793	-	-
2015-03-03T21:37:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.510	-	-
2015-10-27T09:37:29	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.019	-	-
2017-07-22T20:28:36	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.038	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.938 GHz-days
Estimated T-Level:	1.600

Digits	B1	Curves	Complete	FacMiss
20	11000	32 / 100	0.320	72.498%
25	50000	32 / 280	0.114	89.182%

New Calculation Method

Total ECM effort:	2.938 GHz-days
Estimated T-Level:	1.600

Digits	B1	Complete	FacMiss
20	11000	1.032	35.620%
25	50000	0.093	91.093%
30	250000	0.006	99.427%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		30	2.754
50000	5000000	111793594203498544935497	2	0.184

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-14T05:01:00	alan145	Bear4	50000	5000000						3	0.275
2010-03-22T07:46:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.275
2012-06-05T14:07:00	Lukasz Wrobel	i-1	50000	5000000						3	0.275
2014-02-04T15:40:00	Lukasz Wrobel	i-1	50000	5000000						3	0.275
2015-07-22T00:12:00	guru	w1	50000	5000000						3	0.275
2016-02-24T19:56:23	Jason U	Server7	50000	5000000						3	0.275
2016-06-22T15:15:55	Bruce	test	50000	5000000						3	0.275
2017-02-23T03:55:45	Bruce	eleven	50000	5000000						3	0.275
2017-08-04T21:14:48	AnthonyRais	Win10Test	50000	5000000						3	0.275
2017-12-17T20:31:38	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.275
2018-07-17T00:20:51	Chang Chia-Tche	ex-ctcpc	50000	5000000	111793594203498544935497	76.565	2	2		2	0.184

date	userid	compid	res64	spent (GHz-days)
1999-05-09T00:00:00	ANONYMOUS	v4_computers	B9D69246221B664C	0.172

date

userid

compid

res64

spent (GHz-days)

1999-05-09T00:00:00

ANONYMOUS

v4_computers

B9D69246221B664C

0.172

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 = 595000, B2 = 16065000 (P-1 stage 2)

B1 = 595000 (P-1 stage 1)

B1 = 247516 (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

10⁸

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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