M14254369 Mersenne number exponent details

Residue

Status

L-L

0A22E91194A57F6A

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	2.0845	64.1791%	205000	205000	0.1423	1.8502%	2.2269	64.8419%	0.6628%
PrimeNet	2⁶⁵	0.5118	63.0769%	60000	1900000	0.1113	4.0125%	0.6231	64.5585%	1.4815%
GPU72	2⁶⁹	8.3755	65.2174%	100000	2400000	0.1565	2.9182%	8.5319	66.2324%	1.0150%
Difference	-2	-6.2909	-1.0383%	+105000	-2195000	-0.0141	-1.0680%	-6.3050	-1.3905%	-1.3905%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

2.0845

64.1791%

205000

0.1423

1.8502%

2.2269

64.8419%

0.6628%

PrimeNet

2⁶⁵

0.5118

63.0769%

60000

1900000

0.1113

4.0125%

0.6231

64.5585%

1.4815%

GPU72

2⁶⁹

8.3755

65.2174%

100000

2400000

0.1565

2.9182%

8.5319

66.2324%

1.0150%

Difference

-2

-6.2909

-1.0383%

+105000

-2195000

-0.0141

-1.0680%

-6.3050

-1.3905%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
14254369	39592614083295935157038089	26	85.033	1388788731486323076 2² × 3 × 7 × 13 × 1271784552643153	2016-10-01	13	1271784552643153	639,660	48,114,436	89,864,367

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

14254369

39592614083295935157038089

85.033

1388788731486323076
2² × 3 × 7 × 13 × 1271784552643153

2016-10-01

1271784552643153

639,660

48,114,436

89,864,367

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-12-22T00:00:00	ANONYMOUS	v4_computers	205000	205000		-		-	-	0.142	-	-	1.850%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-08-17T00:00:00	Net_Force	v4_computers	2¹	2⁵⁶		-	-	0.001	-	-
2000-10-22T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁵		-	-	0.512	-	-
2014-08-01T14:11:00	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.524	-	-
2015-08-31T08:32:00	Tha	Manual testing	2⁶⁶	2⁶⁷		-	-	1.048	-	-

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	39592614083295935157038089	1	0.728

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-10-02T00:25:32	Bruce	Desk2	50000	5000000	39592614083295935157038089	85.033	1	2		1	0.728

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-03-10T00:00:00	ANONYMOUS	v4_computers	0A22E91194A57F6A	6.826
2005-05-28T00:00:00	ANONYMOUS	v4_computers	0A22E91194A57F6A	6.826

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 = 205000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

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