M11933807 Mersenne number exponent details

Residue

Status

L-L

13BB3E1E7C750CA8

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	2⁷¹	40.0608	66.1972%	6189107	185673210	8.9141	8.3513%	48.9749	69.0202%	2.8230%
PrimeNet	2⁶⁴	0.2983	62.5000%	55000	1500000	0.0747	4.1105%	0.3729	64.0414%	1.5414%
GPU72	2⁶⁸	4.9946	64.7059%	80000	2000000	0.1031	2.9386%	5.0977	65.7431%	1.0372%
Difference	+3	+35.0662	+1.4913%	+6109107	+183673210	+8.8110	+5.4127%	+43.8772	+3.2771%	+3.2771%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷¹

40.0608

66.1972%

6189107

185673210

8.9141

8.3513%

48.9749

69.0202%

2.8230%

PrimeNet

2⁶⁴

0.2983

62.5000%

55000

1500000

0.0747

4.1105%

0.3729

64.0414%

1.5414%

GPU72

2⁶⁸

4.9946

64.7059%

80000

2000000

0.1031

2.9386%

5.0977

65.7431%

1.0372%

Difference

+35.0662

+1.4913%

+6109107

+183673210

+8.8110

+5.4127%

+43.8772

+3.2771%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-08-24T00:00:00	ANONYMOUS	v4_computers	115000	546250		-		-	-	0.077	-	-	1.533%
2016-04-23T01:06:02	Tha	Manual testing	300000	6000000	6	-		-	-	0.341	-	-	3.345%
2021-07-15T01:57:12	LaurV	Manual testing	4316189	127521607		-		-	-	6.157	-	-	7.697%
2021-08-12T01:26:34	LaurV	Manual testing	6189107	185673210		-		-	-	8.914	-	-	8.351%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-02-16T00:00:00	Mark Blanke	v4_computers	2¹	2⁶⁴		-	-	0.298	-	-
2013-10-08T07:39:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.313	-	-
2013-10-20T06:14:00	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.626	-	-
2016-03-06T05:39:24	Yxinity	Manual testing	2⁶⁶	2⁶⁷		-	-	1.252	-	-
2018-01-01T21:55:35	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	2.505	-	-
2018-01-01T21:55:35	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	5.009	-	-
2021-05-18T11:48:09	lycorn	Manual testing	2⁶⁹	2⁷⁰		-	-	10.02	-	-
2021-08-17T05:31:51	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	20.04	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.171 GHz-days
Estimated T-Level:	0.100

Digits	B1	Curves	Complete	FacMiss
20	11000	2 / 100	0.020	98.010%
25	50000	2 / 280	0.007	99.287%

New Calculation Method

Total ECM effort:	1.171 GHz-days
Estimated T-Level:	0.100

Digits	B1	Complete	FacMiss
20	11000	0.065	93.752%
25	50000	0.006	99.419%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		2	1.171

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-02-11T15:40:34	Bruce	Desk2	50000	5000000						1	0.585
2017-09-22T21:57:26	Oliver Kruse	ECM-HTC	50000	5000000						1	0.585

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2001-09-30T00:00:00	ANONYMOUS	v4_computers	13BB3E1E7C750CA8	4.595
2004-05-11T00:00:00	ANONYMOUS	v4_computers	13BB3E1E7C750CA8	4.595

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 = 6189107, B2 = 185673210 (P-1 stage 2)

B1 = 4316189, B2 = 127521607 (P-1 stage 2)

B1 = 6189107 (P-1 stage 1)

B1 = 4316189 (P-1 stage 1)

B1 = 300000, B2 = 6000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 115000, B2 = 546250 (P-1 stage 2)

B1 = 115000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁷

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

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