M8712713 Mersenne number exponent details

Residue

Status

L-L

054B56051DB630B5

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	3.4104	64.1791%	160000	3320000	0.1258	3.9436%	3.5362	65.5918%	1.4126%
PrimeNet	2⁶⁴	0.4085	62.5000%	36000	1000000	0.0335	3.3097%	0.4420	63.7411%	1.2411%
GPU72	2⁶⁸	6.8411	64.7059%	55000	1200000	0.0444	2.2975%	6.8856	65.5168%	0.8109%
Difference	-1	-3.4307	-0.5268%	+105000	+2120000	+0.0813	+1.6461%	-3.3494	+0.0750%	+0.0750%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

3.4104

64.1791%

160000

3320000

0.1258

3.9436%

3.5362

65.5918%

1.4126%

PrimeNet

2⁶⁴

0.4085

62.5000%

36000

1000000

0.0335

3.3097%

0.4420

63.7411%

1.2411%

GPU72

2⁶⁸

6.8411

64.7059%

55000

1200000

0.0444

2.2975%

6.8856

65.5168%

0.8109%

Difference

-1

-3.4307

-0.5268%

+105000

+2120000

+0.0813

+1.6461%

-3.3494

+0.0750%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
8712713	532817346388756112777	21	68.852	30577005485476 2² × 11329 × 674750761	2013-12-28	11329	674750761	11.855	13.923	25.996

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

8712713

532817346388756112777

68.852

30577005485476
2² × 11329 × 674750761

2013-12-28

11329

674750761

11.855

13.923

25.996

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-12-02T00:00:00	ANONYMOUS	v4_computers	45000	720000		-		-	-	0.031	-	-	2.195%
2002-12-09T00:00:00	ANONYMOUS	v4_computers	45000	720000		-		-	-	0.031	-	-	2.195%
2012-05-25T19:24:00	James Heinrich	i7-920	160000	3320000		-		-	-	0.126	-	-	3.944%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-10-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.071	-	-
1998-12-06T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.071	-	-
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.183	-	-
1999-10-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.409	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:

0.000 GHz-days

Digits	B1	Curves	Complete	FacMiss

New Calculation Method

Total ECM effort:

0.000 GHz-days

Digits	B1	Complete	FacMiss

ECM Summary

B1	B2	factor	curves	GHz-days
		532817346388756112777	1	0.00000e+0

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2013-12-28T13:45:00	Sid & Andy	Woody			532817346388756112777	68.852		1		1	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-12-15T00:00:00	ANONYMOUS	v4_computers	054B56051DB630B5	2.275
2002-12-09T00:00:00	ANONYMOUS	v4_computers	054B56051DB630B5	2.275

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-01-02T09:08:39

Oliver Kruse

GTX-2

532817346388756112777

47FD988FD979EB__

2020-08-25T16:14:31

marssystems

system11

532817346388756112777

47FD988FD979EBAE

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 = 160000, B2 = 3320000 (P-1 stage 2)

B1 = 160000 (P-1 stage 1)

B1 = 45000, B2 = 720000 (P-1 stage 2)

B1 = 45000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁷

2⁶⁴

2⁶³

2⁶²

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