M14976259 Mersenne number exponent details

Residue

Status

L-L

664C7C23F77C7205

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	1.9841	64.1791%	225000	225000	0.1562	1.9454%	2.1403	64.8760%	0.6969%
PrimeNet	2⁶⁵	0.4872	63.0769%	65000	2000000	0.1183	4.1420%	0.6055	64.6063%	1.5294%
GPU72	2⁶⁹	7.9717	65.2174%	100000	2600000	0.1640	2.9926%	8.1358	66.2583%	1.0409%
Difference	-2	-5.9877	-1.0383%	+125000	-2375000	-0.0078	-1.0472%	-5.9955	-1.3823%	-1.3823%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

1.9841

64.1791%

225000

0.1562

1.9454%

2.1403

64.8760%

0.6969%

PrimeNet

2⁶⁵

0.4872

63.0769%

65000

2000000

0.1183

4.1420%

0.6055

64.6063%

1.5294%

GPU72

2⁶⁹

7.9717

65.2174%

100000

2600000

0.1640

2.9926%

8.1358

66.2583%

1.0409%

Difference

-2

-5.9877

-1.0383%

+125000

-2375000

-0.0078

-1.0472%

-5.9955

-1.3823%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
14976259	9375690515712396562769	22	72.989	313018441912376 2³ × 61 × 67807 × 9459661	2016-11-21	67807	9459661	117.72	0.4024	0.6684

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

14976259

9375690515712396562769

72.989

313018441912376
2³ × 61 × 67807 × 9459661

2016-11-21

67807

9459661

117.72

0.4024

0.6684

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-02-24T00:00:00	ANONYMOUS	v4_computers	225000	225000		-		-	-	0.156	-	-	1.945%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-08-24T00:00:00	Net_Force	v4_computers	2¹	2⁵⁷		-	-	0.001	-	-
2000-09-08T00:00:00	Net_Force	v4_computers	2¹	2⁵⁸		-	-	0.003	-	-
2000-09-29T00:00:00	Net_Force	v4_computers	2¹	2⁵⁹		-	-	0.005	-	-
2000-12-31T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.238	-	-
2001-01-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁵		-	-	0.487	-	-
2016-03-16T02:31:57	Mark Rose	Manual testing	2⁶⁵	2⁶⁶		-	-	0.499	-	-
2015-10-25T10:22:37	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.998	-	-

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	9375690515712396562769	1	0.728

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-11-22T04:05:46	Bruce	Desk2	50000	5000000	9375690515712396562769	72.989	1	2		1	0.728

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-06-23T00:00:00	ANONYMOUS	v4_computers	664C7C23F77C7205	7.172
2006-03-28T00:00:00	ANONYMOUS	v4_computers	664C7C23F77C7205	7.172

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 = 225000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁵⁹

2⁵⁸

2⁵⁷

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