M2385113 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	12.4581	67.1642%	2000000	60000000	0.5055	7.6104%	12.9635	69.6631%	2.4989%
PrimeNet	2⁵⁹	0.0322	62.7119%	10000	170000	0.0018	2.4767%	0.0340	63.6354%	0.9235%
GPU72	2⁶³	0.6692	65.0794%	10000	140000	0.0017	1.2732%	0.6708	65.5240%	0.4446%
Difference	+4	+11.7889	+2.0848%	+1990000	+59860000	+0.5038	+6.3372%	+12.2927	+4.1391%	+4.1391%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.4581

67.1642%

2000000

60000000

0.5055

7.6104%

12.9635

69.6631%

2.4989%

PrimeNet

2⁵⁹

0.0322

62.7119%

10000

170000

0.0018

2.4767%

0.0340

63.6354%

0.9235%

GPU72

2⁶³

0.6692

65.0794%

10000

140000

0.0017

1.2732%

0.6708

65.5240%

0.4446%

Difference

+11.7889

+2.0848%

+1990000

+59860000

+0.5038

+6.3372%

+12.2927

+4.1391%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2385113	14310679	8	23.771	3 3	-	1	3	4.688e-13	1.086e-7	1.994e-7
2385113	2587041436807	13	41.234	542331 3² × 60259	2008-07-14	9	60259	1.704e-7	0.0003	0.0006

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2385113

14310679

23.771

3
3

4.688e-13

1.086e-7

1.994e-7

2385113

2587041436807

41.234

542331
3² × 60259

2008-07-14

60259

1.704e-7

0.0003

0.0006

exponent	prime factors	composite factor	digits	bits*
2385113	14310679 2587041436807	37022319561843761953	20	65.005

exponent

prime factors

composite factor

digits

bits*

2385113

14310679
2587041436807

37022319561843761953

65.005

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2018-09-28T16:24:27	alpertron	Manual testing	2000000	60000000	12	-	skipped known factor: 14310679 skipped known factor: 2587041436807	-	-	0.505	-	-	7.610%

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.267 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.267 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
		2587041436807	1	0.00000e+0
50000	5000000		3	0.267

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-14T20:23:00	George Woltman	Manual testing			2587041436807	41.234		1		1	-
2018-02-16T02:42:30	Oliver Kruse	ECM-HTC	50000	5000000						3	0.267

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-12T13:14:55

Chang Chia-Tche

homura

14310679

2587041436807

D0B228388B155A__

2017-11-02T13:58:32

Oliver Kruse

GTX-0

14310679

2587041436807

D0B228388B155A__

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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

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