M13948411 Mersenne number exponent details

Residue

Status

L-L

A13889450FF807CF

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	2.1303	64.1791%	150000	1837500	0.1556	3.6519%	2.2859	65.4873%	1.3082%
PrimeNet	2⁶⁵	0.5230	63.0769%	60000	1900000	0.1031	3.9998%	0.6261	64.5538%	1.4768%
GPU72	2⁶⁹	8.5592	65.2174%	90000	2400000	0.1389	2.8515%	8.6980	66.2092%	0.9918%
Difference	-2	-6.4289	-1.0383%	+60000	-562500	+0.0168	+0.8004%	-6.4121	-0.7220%	-0.7220%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

2.1303

64.1791%

150000

1837500

0.1556

3.6519%

2.2859

65.4873%

1.3082%

PrimeNet

2⁶⁵

0.5230

63.0769%

60000

1900000

0.1031

3.9998%

0.6261

64.5538%

1.4768%

GPU72

2⁶⁹

8.5592

65.2174%

90000

2400000

0.1389

2.8515%

8.6980

66.2092%

0.9918%

Difference

-2

-6.4289

-1.0383%

+60000

-562500

+0.0168

+0.8004%

-6.4121

-0.7220%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
13948411	16682791118329376096489	23	73.821	598017620728604 2² × 59 × 15889 × 159479701	2016-08-31	15889	159479701	239.97	5.5996	10.440

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

13948411

16682791118329376096489

73.821

598017620728604
2² × 59 × 15889 × 159479701

2016-08-31

15889

159479701

239.97

5.5996

10.440

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-03-24T00:00:00	Todd A. Hayes	v4_computers	150000	1837500		-		-	-	0.156	-	-	3.652%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-08-01T00:00:00	lalera	v4_computers	2¹	2⁵⁴		-	-	0.000	-	-
2000-08-17T00:00:00	Ed Straker	v4_computers	2¹	2⁶⁵		-	-	0.523	-	-
2014-07-15T13:19:00	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.536	-	-
2015-09-13T10:58:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	1.071	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.675 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:	0.675 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	16682791118329376096489	1	0.675

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-08-31T10:09:14	Bruce	Desk2	50000	5000000	16682791118329376096489	73.821	1	2		1	0.675

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-04-28T00:00:00	Todd A. Hayes	v4_computers	A13889450FF807CF	6.189
2005-03-20T00:00:00	ANONYMOUS	v4_computers	A13889450FF807CF	6.189

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 = 150000, B2 = 1837500 (P-1 stage 2)

B1 = 150000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

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