M2288687 Mersenne number exponent details

Residue

Status

L-L

6D24B13FBA078F34

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	12.9830	67.1642%	500000	15000000	0.1264	5.2067%	13.1093	68.8738%	1.7097%
PrimeNet	2⁵⁸	0.0168	62.0690%	10000	190000	0.0019	2.9253%	0.0187	63.1786%	1.1096%
GPU72	2⁶²	0.2684	64.5161%	12000	200000	0.0022	1.7359%	0.2706	65.1321%	0.6160%
Difference	+5	+12.7145	+2.6481%	+488000	+14800000	+0.1242	+3.4708%	+12.8387	+3.7418%	+3.7418%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.9830

67.1642%

500000

15000000

0.1264

5.2067%

13.1093

68.8738%

1.7097%

PrimeNet

2⁵⁸

0.0168

62.0690%

10000

190000

0.0019

2.9253%

0.0187

63.1786%

1.1096%

GPU72

2⁶²

0.2684

64.5161%

12000

200000

0.0022

1.7359%

0.2706

65.1321%

0.6160%

Difference

+12.7145

+2.6481%

+488000

+14800000

+0.1242

+3.4708%

+12.8387

+3.7418%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2288687	5811285670421480593	19	62.334	1269567588408 2³ × 3 × 7 × 13697 × 551723	2010-01-05	13697	551723	0.4010	0.0042	0.0055

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2288687

5811285670421480593

62.334

1269567588408
2³ × 3 × 7 × 13697 × 551723

2010-01-05

13697

551723

0.4010

0.0042

0.0055

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-05-04T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.284%
2016-04-19T11:25:38	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 5811285670421480593	-	-	0.126	-	-	5.207%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-01-11T01:51:00	Sturle Sunde	hindemith.ifi	2⁶⁰	2⁶¹		-	-	0.067	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.265 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:	0.265 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
		5811285670421480593	1	0.00000e+0
50000	5000000		3	0.265

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-13T22:50:00	Smurgs	Praca	50000	5000000						3	0.265
2010-01-05T18:17:00	SubPrime	abd0			5811285670421480593	62.334		1		1	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-23T00:00:00	arnaud	v4_computers	6D24B13FBA078F34	0.155
1999-09-07T00:00:00	ANONYMOUS	v4_computers	6D24B13FBA078F34	0.155

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-12T18:06:21

kkmrkkblmbrbk

c4.xlarge

9D1C2FE0203EB2__

2017-10-30T05:53:35

Oliver Kruse

GTX-3

5811285670421480593

9D1C2FE0203EB2__

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

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