M15491027 Mersenne number exponent details

Residue

Status

L-L

1FFD8BC6143ADA56

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	1.9181	64.1791%	175000	2012500	0.2001	3.8600%	2.1182	65.5618%	1.3827%
PrimeNet	2⁶⁵	0.4710	63.0769%	70000	2200000	0.1353	4.2985%	0.6063	64.6640%	1.5871%
GPU72	2⁶⁹	7.7068	65.2174%	110000	2800000	0.1866	3.1104%	7.8934	66.2993%	1.0819%
Difference	-2	-5.7887	-1.0383%	+65000	-787500	+0.0135	+0.7495%	-5.7752	-0.7375%	-0.7375%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

1.9181

64.1791%

175000

2012500

0.2001

3.8600%

2.1182

65.5618%

1.3827%

PrimeNet

2⁶⁵

0.4710

63.0769%

70000

2200000

0.1353

4.2985%

0.6063

64.6640%

1.5871%

GPU72

2⁶⁹

7.7068

65.2174%

110000

2800000

0.1866

3.1104%

7.8934

66.2993%

1.0819%

Difference

-2

-5.7887

-1.0383%

+65000

-787500

+0.0135

+0.7495%

-5.7752

-0.7375%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
15491027	38658809825964866849191	23	75.033	1247780725769985 3 × 5 × 11 × 7562307428909	2016-12-18	11	7562307428909	652.73	299,624	559,614

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

15491027

38658809825964866849191

75.033

1247780725769985
3 × 5 × 11 × 7562307428909

2016-12-18

7562307428909

652.73

299,624

559,614

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-05-05T00:00:00	dakruger	v4_computers	175000	2012500		-		-	-	0.200	-	-	3.860%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-01-14T00:00:00	Net_Force	v4_computers	2¹	2⁵⁸		-	-	0.002	-	-
2001-03-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁵		-	-	0.471	-	-
2014-02-23T00:23:00	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.482	-	-
2014-02-23T00:23:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.965	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.763 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:	0.763 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	38658809825964866849191	1	0.763

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-12-19T02:29:04	Bruce	mini	50000	5000000	38658809825964866849191	75.033	1	2		1	0.763

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2004-05-25T00:00:00	Architects Cubed	v4_computers	1FFD8BC6143ADA56	7.769
2005-11-27T00:00:00	ANONYMOUS	v4_computers	1FFD8BC6143ADA56	7.769

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 = 175000, B2 = 2012500 (P-1 stage 2)

B1 = 175000 (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

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