M27315259 Mersenne number exponent details

Residue

Status

L-L

FFAA276FCB07240A

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	2⁷¹	17.5022	64.7887%	415000	415000	0.5570	1.7286%	18.0593	65.3974%	0.6087%
PrimeNet	2⁶⁶	0.5407	62.1212%	120000	4500000	0.4814	5.2168%	1.0220	64.0973%	1.9761%
GPU72	2⁷⁰	8.7479	64.2857%	200000	6000000	0.6926	3.9072%	9.4405	65.6811%	1.3954%
Difference	+1	+8.7544	+0.5030%	+215000	-5585000	-0.1356	-2.1786%	+8.6188	-0.2837%	-0.2837%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷¹

17.5022

64.7887%

415000

0.5570

1.7286%

18.0593

65.3974%

0.6087%

PrimeNet

2⁶⁶

0.5407

62.1212%

120000

4500000

0.4814

5.2168%

1.0220

64.0973%

1.9761%

GPU72

2⁷⁰

8.7479

64.2857%

200000

6000000

0.6926

3.9072%

9.4405

65.6811%

1.3954%

Difference

+8.7544

+0.5030%

+215000

-5585000

-0.1356

-2.1786%

+8.6188

-0.2837%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
27315259	177942052645377257009	21	67.270	3257191386056 2³ × 407148923257	2011-10-05	8	407148923257	1.6695	29,775	55,611

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

27315259

177942052645377257009

67.270

3257191386056
2³ × 407148923257

2011-10-05

407148923257

1.6695

29,775

55,611

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2005-11-13T00:00:00	Fabrice Bellet	v4_computers	415000	415000		-		-	-	0.557	-	-	1.729%
2011-10-05T10:10:00	Carsten Kossendey	Manual testing	415000	415000			177942052645377257009	21	67.270	0.557	50.57	1.114	1.729%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-11-05T00:00:00	Jocelyn Larouche	v4_computers	2¹	2⁵⁴		-	-	8.78574e-5	-	-
2001-08-18T00:00:00	Net_Force	v4_computers	2¹	2⁵⁶		-	-	0.000	-	-
2004-04-09T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.011	-	-
2004-07-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.022	-	-
2005-01-20T00:00:00	Vaxman	v4_computers	2¹	2⁶⁷		-	-	1.088	-	-
2011-10-05T10:09:00	Carsten Kossendey	Manual testing	2⁶⁷	2⁷¹	MISSED FACTOR!	-	-	16.41	-	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2005-12-12T00:00:00	Fabrice Bellet	v4_computers	FFAA276FCB07240A	25.29

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 = 415000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁷¹

2⁶⁷

2⁶²

2⁶¹

2⁵⁶

2⁵⁴

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