M2567179 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	11.5745	67.1642%	-	-	-	-	11.5745	67.1642%	0.0000%
PrimeNet	2⁵⁹	0.0299	62.7119%	11000	200000	0.0021	2.6886%	0.0321	63.7144%	1.0025%
GPU72	2⁶³	0.6217	65.0794%	12000	180000	0.0021	1.4800%	0.6238	65.5962%	0.5168%
Difference	+4	+10.9528	+2.0848%	-12000	-180000	-0.0021	-1.4800%	+10.9507	+1.5680%	+1.5680%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

11.5745

67.1642%

11.5745

67.1642%

0.0000%

PrimeNet

2⁵⁹

0.0299

62.7119%

11000

200000

0.0021

2.6886%

0.0321

63.7144%

1.0025%

GPU72

2⁶³

0.6217

65.0794%

12000

180000

0.0021

1.4800%

0.6238

65.5962%

0.5168%

Difference

+10.9528

+2.0848%

-12000

-180000

-0.0021

-1.4800%

+10.9507

+1.5680%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2567179	25671791	8	24.614	5 5	-	1	5	8.716e-13	1.225e-7	2.047e-7
2567179	444709257772411039	18	58.626	86614384461 3 × 11 × 2624678317	2015-09-18	11	2624678317	0.0189	14.382	26.862

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2567179

25671791

24.614

5
5

8.716e-13

1.225e-7

2.047e-7

2567179

444709257772411039

58.626

86614384461
3 × 11 × 2624678317

2015-09-18

2624678317

0.0189

14.382

26.862

exponent	prime factors	composite factor	digits	bits*
2567179	25671791 444709257772411039	11416483121298461759300849	26	83.239

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2015-09-18T11:39:00	TJAOI	Manual testing	2⁵⁸	2⁵⁹*	444709257772411039	58.626	18	0.004	0.361	0.008

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.277 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:	0.277 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
50000	5000000		3	0.277

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-03-21T19:46:46	Flash Jone	sa-east1-b	50000	5000000						3	0.277

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:28:32

alpertron

Manual testing

25671791

444709257772411039

EDE427B6E1EFA5__

2017-11-11T08:15:56

Oliver Kruse

GTX-1

25671791

444709257772411039

EDE427B6E1EFA5__

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

10⁰

10¹

10²

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁷

2⁵⁹

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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