M13948397 Mersenne number exponent details

Residue

Status

L-L

F5355DACDD4348C1

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	2⁷²	68.5623	66.6667%	165000	3135000	0.2103	2.4030%	68.7725	67.4677%	0.8010%
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	+3	+60.0031	+1.4493%	+75000	+735000	+0.0714	-0.4485%	+60.0745	+1.2584%	+1.2584%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

68.5623

66.6667%

165000

3135000

0.2103

2.4030%

68.7725

67.4677%

0.8010%

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

+60.0031

+1.4493%

+75000

+735000

+0.0714

-0.4485%

+60.0745

+1.2584%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-12-08T00:00:00	ANONYMOUS	v4_computers	165000	3135000		-		-	-	0.210	-	-	2.403%

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	ANONYMOUS	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	-	-
2017-12-22T04:01:22	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	2.143	-	-
2018-01-29T09:55:12	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	4.286	-	-
2021-08-09T19:57:29	SRBase	Manual testing	2⁶⁹	2⁷⁰		-	-	8.572	-	-
2021-09-05T07:13:25	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	17.14	-	-
2021-10-25T13:05:47	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	34.29	-	-

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	0.038	96.227%
25	50000	0.004	99.645%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		1	0.675

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-08-30T02:27:36	Summy	WDG	50000	5000000						1	0.675

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-01-08T00:00:00	ANONYMOUS	v4_computers	F5355DACDD4348C1	6.189
2005-05-12T00:00:00	ANONYMOUS	v4_computers	F5355DACDD4348C1	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 = 165000, B2 = 3135000 (P-1 stage 2)

B1 = 165000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁴

10⁵

10⁶

10⁷

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

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