M13782701 Mersenne number exponent details

Residue

Status

L-L

7298EB5E4DF7A35D

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	69.3865	66.6667%	155000	2170000	0.1703	2.1691%	69.5569	67.3897%	0.7230%
PrimeNet	2⁶⁵	0.5293	63.0769%	60000	1900000	0.1031	3.9928%	0.6324	64.5512%	1.4743%
GPU72	2⁶⁹	8.6621	65.2174%	90000	2200000	0.1319	2.7911%	8.7939	66.1882%	0.9708%
Difference	+3	+60.7244	+1.4493%	+65000	-30000	+0.0385	-0.6219%	+60.7629	+1.2015%	+1.2015%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

69.3865

66.6667%

155000

2170000

0.1703

2.1691%

69.5569

67.3897%

0.7230%

PrimeNet

2⁶⁵

0.5293

63.0769%

60000

1900000

0.1031

3.9928%

0.6324

64.5512%

1.4743%

GPU72

2⁶⁹

8.6621

65.2174%

90000

2200000

0.1319

2.7911%

8.7939

66.1882%

0.9708%

Difference

+60.7244

+1.4493%

+65000

-30000

+0.0385

-0.6219%

+60.7629

+1.2015%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-11-24T00:00:00	ANONYMOUS	v4_computers	155000	2170000		-		-	-	0.170	-	-	2.169%
2001-12-22T00:00:00	ANONYMOUS	v4_computers	155000	2170000		-		-	-	0.170	-	-	2.169%
2002-01-28T00:00:00	ANONYMOUS	v4_computers	155000	2170000		-		-	-	0.170	-	-	2.169%
2002-02-10T00:00:00	ANONYMOUS	v4_computers	155000	2170000		-		-	-	0.170	-	-	2.169%
2002-12-02T00:00:00	ANONYMOUS	v4_computers	155000	2170000		-		-	-	0.170	-	-	2.169%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-07-25T00:00:00	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	-	-
2018-01-07T23:29:59	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	4.337	-	-
2021-08-08T08:14:43	SRBase	Manual testing	2⁶⁹	2⁷⁰		-	-	8.675	-	-
2021-09-04T07:04:58	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	17.35	-	-
2021-09-23T09:04:02	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
2016-08-07T04:18:12	Bruce	Desk2	50000	5000000						1	0.675

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-01-28T00:00:00	ANONYMOUS	v4_computers	7298EB5E4DF7A35D	6.115
2002-02-10T00:00:00	ANONYMOUS	v4_computers	7298EB5E4DF7A35D	6.115
2002-12-02T00:00:00	ANONYMOUS	v4_computers	7298EB5E4DF7A35D	6.115
2005-02-18T00:00:00	Sturle Sunde	v4_computers	7298EB5E4DF7A35D	6.115
2005-03-06T00:00:00	Sturle Sunde	v4_computers	7298EB5E4DF7A35D	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 = 155000, B2 = 2170000 (P-1 stage 2)

B1 = 155000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁴

10⁵

10⁶

10⁷

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

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