M13782371 Mersenne number exponent details

Residue

Status

L-L

F962FC723FC215DC

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	69.3882	66.6667%	300000	6000000	0.3928	3.0689%	69.7810	67.6896%	1.0230%
PrimeNet	2⁶⁵	0.5294	63.0769%	60000	1900000	0.1031	3.9928%	0.6324	64.5512%	1.4742%
GPU72	2⁶⁹	8.6623	65.2174%	90000	2200000	0.1319	2.7911%	8.7941	66.1882%	0.9708%
Difference	+3	+60.7259	+1.4493%	+210000	+3800000	+0.2609	+0.2778%	+60.9868	+1.5014%	+1.5014%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

69.3882

66.6667%

300000

6000000

0.3928

3.0689%

69.7810

67.6896%

1.0230%

PrimeNet

2⁶⁵

0.5294

63.0769%

60000

1900000

0.1031

3.9928%

0.6324

64.5512%

1.4742%

GPU72

2⁶⁹

8.6623

65.2174%

90000

2200000

0.1319

2.7911%

8.7941

66.1882%

0.9708%

Difference

+60.7259

+1.4493%

+210000

+3800000

+0.2609

+0.2778%

+60.9868

+1.5014%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-02-10T00:00:00	ANONYMOUS	v4_computers	130000	585000		-		-	-	0.100	-	-	1.444%
2016-04-18T08:00:20	Tha	Riet-Ubuntu	300000	6000000	12	-		-	-	0.393	-	-	3.069%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-07-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.258	-	-
2000-08-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁵		-	-	0.529	-	-
2014-07-02T04:17:00	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.542	-	-
2015-08-20T10:16:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	1.084	-	-
2017-12-22T13:48:42	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	2.169	-	-
2018-01-14T22:54:48	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	4.338	-	-
2021-08-09T19:18:47	SRBase	Manual testing	2⁶⁹	2⁷⁰		-	-	8.675	-	-
2021-09-06T18:08:08	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	17.35	-	-
2021-09-29T01:49:02	Dylan Delgado	GPU72_TF	2⁷¹	2⁷²		-	-	34.70	-	-

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		1	0.675

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-08-04T18:31:11	XZT	Laptop	50000	5000000						1	0.675

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-03-31T00:00:00	ANONYMOUS	v4_computers	F962FC723FC215DC	6.115
2005-03-06T00:00:00	ANONYMOUS	v4_computers	F962FC723FC215DC	6.115

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 = 130000, B2 = 585000 (P-1 stage 2)

B1 = 130000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁴

10⁵

10⁶

10⁷

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

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