M2376293 Mersenne number exponent details

Residue

Status

L-L

57DACD8F5A36DE45

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	12.5043	67.1642%	2000000	60000000	0.5055	7.6075%	13.0098	69.6622%	2.4980%
PrimeNet	2⁵⁹	0.0323	62.7119%	10000	170000	0.0018	2.4750%	0.0342	63.6347%	0.9229%
GPU72	2⁶³	0.6716	65.0794%	10000	140000	0.0017	1.2722%	0.6733	65.5236%	0.4443%
Difference	+4	+11.8327	+2.0848%	+1990000	+59860000	+0.5038	+6.3353%	+12.3365	+4.1385%	+4.1385%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.5043

67.1642%

2000000

60000000

0.5055

7.6075%

13.0098

69.6622%

2.4980%

PrimeNet

2⁵⁹

0.0323

62.7119%

10000

170000

0.0018

2.4750%

0.0342

63.6347%

0.9229%

GPU72

2⁶³

0.6716

65.0794%

10000

140000

0.0017

1.2722%

0.6733

65.5236%

0.4443%

Difference

+11.8327

+2.0848%

+1990000

+59860000

+0.5038

+6.3353%

+12.3365

+4.1385%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2376293	327374672826697461697	21	68.150	68883482135136 2⁵ × 3 × 52813 × 13586357	2015-06-21	52813	13586357	50.110	0.0774	0.1354

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2376293

327374672826697461697

68.150

68883482135136
2⁵ × 3 × 52813 × 13586357

2015-06-21

52813

13586357

50.110

0.0774

0.1354

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-21T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.287%
2010-11-07T17:04:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.243%
2010-11-15T22:51:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.310%
2010-12-29T07:19:00	markr	tiny	100000	2025000		-		-	-	0.020	-	-	2.713%
2014-09-10T00:51:00	Jocelyn Larouche	Manual testing	127010	127010		-		-	-	0.012	-	-	1.074%
2018-09-28T16:24:32	alpertron	Manual testing	2000000	60000000	12	-	skipped known factor: 327374672826697461697	-	-	0.505	-	-	7.607%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-07-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.032	-	-
2022-03-09T16:37:54	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.065	-	-
2009-01-15T00:50:00	Sturle Sunde	golli.ifi	2⁶⁰	2⁶¹		-	-	0.065	-	-
2012-05-31T16:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.129	-	-
2013-01-23T08:26:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.413	-	-
2015-03-09T12:35:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.826	-	-
2015-03-09T12:35:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.572	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.156 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:	1.156 GHz-days
Estimated T-Level:	0.650

Digits	B1	Complete	FacMiss
20	11000	0.500	60.653%
25	50000	0.046	95.479%
30	250000	0.003	99.709%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.067
50000	5000000	327374672826697461697	1	0.089

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-26T19:58:00	SubPrime	pitr	50000	5000000						3	0.267
2010-02-10T21:21:00	SubPrime	abd0	50000	5000000						3	0.267
2012-01-22T07:11:00	S36049	Wolle5	50000	5000000						3	0.267
2013-11-13T12:40:00	arnaud	srv-630	50000	5000000						3	0.267
2015-06-21T16:42:00	guru	w6	50000	5000000	327374672826697461697	68.150	1	2		1	0.089

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:24:42

alpertron

Manual testing

327374672826697461697

8AA9CD7E8002D8__

2017-11-02T03:08:48

Oliver Kruse

GTX-1

327374672826697461697

8AA9CD7E8002D8__

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 = 100000, B2 = 2025000 (P-1 stage 2)

B1 = 127010 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

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