M15711923 Mersenne number exponent details

Residue

Status

L-L

2908192F2B094A4E

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	1.8912	64.1791%	300000	6000000	0.4841	5.2111%	2.3753	66.0458%	1.8667%
PrimeNet	2⁶⁵	0.4643	63.0769%	70000	2200000	0.1475	4.3072%	0.6119	64.6673%	1.5903%
GPU72	2⁶⁹	7.5985	65.2174%	110000	2800000	0.2034	3.1168%	7.8019	66.3015%	1.0841%
Difference	-2	-5.7073	-1.0383%	+190000	+3200000	+0.2807	+2.0943%	-5.4266	-0.2557%	-0.2557%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

1.8912

64.1791%

300000

6000000

0.4841

5.2111%

2.3753

66.0458%

1.8667%

PrimeNet

2⁶⁵

0.4643

63.0769%

70000

2200000

0.1475

4.3072%

0.6119

64.6673%

1.5903%

GPU72

2⁶⁹

7.5985

65.2174%

110000

2800000

0.2034

3.1168%

7.8019

66.3015%

1.0841%

Difference

-2

-5.7073

-1.0383%

+190000

+3200000

+0.2807

+2.0943%

-5.4266

-0.2557%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
15711923	22873067175869025417857431	26	84.242	727888851538701705 3² × 5 × 34620871 × 467212619	2016-12-27	34620871	467212619	361,891	46.137	55.865

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

15711923

22873067175869025417857431

84.242

727888851538701705
3² × 5 × 34620871 × 467212619

2016-12-27

34620871

467212619

361,891

46.137

55.865

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-05-25T00:00:00	curtisc	v4_computers	235000	235000		-		-	-	0.186	-	-	1.999%
2015-11-28T21:23:28	Tha	Manual testing	300000	6000000	12	-		-	-	0.484	-	-	5.211%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-01-28T00:00:00	Net_Force	v4_computers	2¹	2⁵⁸		-	-	0.002	-	-
2001-05-06T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁵		-	-	0.464	-	-
2016-03-16T02:21:44	Mark Rose	Manual testing	2⁶⁵	2⁶⁶		-	-	0.476	-	-
2014-07-10T09:15:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.951	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.831 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:	0.831 GHz-days
Estimated T-Level:	0.050

Digits	B1	Complete	FacMiss
20	11000	0.038	96.227%
25	50000	0.004	99.645%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	22873067175869025417857431	1	0.831

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-12-27T13:03:52	ATH	ec2-8x	50000	5000000	22873067175869025417857431	84.242	1	2		1	0.831

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-08-03T00:00:00	curtisc	v4_computers	2908192F2B094A4E	8.591
2006-02-15T00:00:00	ANONYMOUS	v4_computers	2908192F2B094A4E	8.591

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 = 300000, B2 = 6000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 235000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁷

10⁸

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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