M15007591 Mersenne number exponent details

Residue

Status

L-L

1687B8D0BA6CB679

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	2⁶⁸	3.9716	64.7059%	170000	2422500	0.2033	3.5865%	4.1749	65.9717%	1.2658%
PrimeNet	2⁶⁵	0.4861	63.0769%	65000	2000000	0.1183	4.1432%	0.6045	64.6067%	1.5298%
GPU72	2⁶⁹	7.9551	65.2174%	100000	2600000	0.1640	2.9935%	8.1191	66.2586%	1.0412%
Difference	-1	-3.9834	-0.5115%	+70000	-177500	+0.0392	+0.5930%	-3.9442	-0.2869%	-0.2869%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

3.9716

64.7059%

170000

2422500

0.2033

3.5865%

4.1749

65.9717%

1.2658%

PrimeNet

2⁶⁵

0.4861

63.0769%

65000

2000000

0.1183

4.1432%

0.6045

64.6067%

1.5298%

GPU72

2⁶⁹

7.9551

65.2174%

100000

2600000

0.1640

2.9935%

8.1191

66.2586%

1.0412%

Difference

-1

-3.9834

-0.5115%

+70000

-177500

+0.0392

+0.5930%

-3.9442

-0.2869%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
15007591	6476091621468863277847	22	72.456	215760531502653 3 × 4297 × 16737299783	2016-11-21	4297	16737299783	74.111	633.21	1,182.7

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

15007591

6476091621468863277847

72.456

215760531502653
3 × 4297 × 16737299783

2016-11-21

4297

16737299783

74.111

633.21

1,182.7

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-03-03T00:00:00	ANONYMOUS	v4_computers	170000	2422500		-		-	-	0.203	-	-	3.587%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-01-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁵		-	-	0.486	-	-
2014-06-11T15:16:00	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.498	-	-
2014-06-11T15:16:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.996	-	-
2015-10-19T17:00:16	mikr	Manual testing	2⁶⁷	2⁶⁸		-	-	1.992	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.728 GHz-days
Estimated T-Level:	0.050

Digits	B1	Curves	Complete	FacMiss
20	11000	1 / 100	0.010	99.000%
25	50000	1 / 280	0.004	99.643%

New Calculation Method

Total ECM effort:	0.728 GHz-days
Estimated T-Level:	0.050

Digits	B1	Complete	FacMiss
20	11000	0.032	96.826%
25	50000	0.003	99.709%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	6476091621468863277847	1	0.728

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-11-21T05:37:04	Bruce	test	50000	5000000	6476091621468863277847	72.456	1	2		1	0.728

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-04-14T00:00:00	ANONYMOUS	v4_computers	1687B8D0BA6CB679	7.187
2006-01-15T00:00:00	georgep	v4_computers	1687B8D0BA6CB679	7.187

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 = 170000, B2 = 2422500 (P-1 stage 2)

B1 = 170000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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