M2392573 Mersenne number exponent details

Residue

Status

L-L

BF63569B9A9E5FFF

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	12.4192	67.1642%	2000000	60000000	0.5055	7.6128%	12.9247	69.6639%	2.4997%
PrimeNet	2⁵⁹	0.0321	62.7119%	10000	170000	0.0018	2.4782%	0.0339	63.6359%	0.9241%
GPU72	2⁶³	0.6671	65.0794%	10000	140000	0.0017	1.2740%	0.6687	65.5243%	0.4449%
Difference	+4	+11.7522	+2.0848%	+1990000	+59860000	+0.5038	+6.3388%	+12.2559	+4.1397%	+4.1397%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.4192

67.1642%

2000000

60000000

0.5055

7.6128%

12.9247

69.6639%

2.4997%

PrimeNet

2⁵⁹

0.0321

62.7119%

10000

170000

0.0018

2.4782%

0.0339

63.6359%

0.9241%

GPU72

2⁶³

0.6671

65.0794%

10000

140000

0.0017

1.2740%

0.6687

65.5243%

0.4449%

Difference

+11.7522

+2.0848%

+1990000

+59860000

+0.5038

+6.3388%

+12.2559

+4.1397%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2392573	2731930575739258097	19	61.245	570918959576 2³ × 7 × 7883 × 1293287	-	7883	1293287	0.1766	0.0076	0.0129

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2392573

2731930575739258097

61.245

570918959576
2³ × 7 × 7883 × 1293287

7883

1293287

0.1766

0.0076

0.0129

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-09T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.287%
2003-02-24T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.003	-	-	0.572%
2003-09-21T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.287%
2018-09-28T16:25:14	alpertron	Manual testing	2000000	60000000	12	-	skipped known factor: 2731930575739258097	-	-	0.505	-	-	7.613%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-05-09T00:00:00	Stephen Wood	v4_computers	2¹	2⁵⁹		-	-	0.032	-	-

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
50000	5000000		3	0.267

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-02-16T00:57:00	ATH	ec2-1xe	50000	5000000						3	0.267

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-05-23T00:00:00	ANONYMOUS	v4_computers	BF63569B9A9E5FFF	0.162
1999-05-30T00:00:00	Stephen Wood	v4_computers	BF63569B9A9E5FFF	0.162

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-12T19:56:31

Oliver Kruse

GTX-0

C05307787A418F__

2017-11-26T01:13:05

kkmrkkblmbrbk

c4.xlarge

2731930575739258097

C05307787A418F__

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 = 4096, B2 = 409600 (P-1 stage 2)

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

B1 = 4096 (P-1 stage 1)

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