M12905407 Mersenne number exponent details

Residue

Status

L-L

7379A86C83E09403

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	74.1033	66.6667%	600000	620747400	20.3671	7.1940%	94.4704	69.0647%	2.3980%
PrimeNet	2⁶⁴	0.2758	62.5000%	60000	1700000	0.0885	4.3326%	0.3643	64.1247%	1.6247%
GPU72	2⁶⁸	4.6186	64.7059%	90000	2400000	0.1278	3.1654%	4.7464	65.8231%	1.1172%
Difference	+4	+69.4847	+1.9608%	+510000	+618347400	+20.2392	+4.0286%	+89.7240	+3.2416%	+3.2416%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

74.1033

66.6667%

600000

620747400

20.3671

7.1940%

94.4704

69.0647%

2.3980%

PrimeNet

2⁶⁴

0.2758

62.5000%

60000

1700000

0.0885

4.3326%

0.3643

64.1247%

1.6247%

GPU72

2⁶⁸

4.6186

64.7059%

90000

2400000

0.1278

3.1654%

4.7464

65.8231%

1.1172%

Difference

+69.4847

+1.9608%

+510000

+618347400

+20.2392

+4.0286%

+89.7240

+3.2416%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-06-17T00:00:00	ANONYMOUS	v4_computers	200000	200000		-		-	-	0.118	-	-	0.943%
2001-09-22T00:00:00	Luigi Morelli	v4_computers	155000	2286250		-		-	-	0.161	-	-	2.176%
2015-05-07T08:35:00	Tha	Manual testing	300000	6000000		-		-	-	0.362	-	-	3.042%
2021-12-24T20:06:57	Luminescence	5950X	600000	620747400		-		-	-	20.37	-	-	7.194%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-04-19T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.276	-	-
2013-06-01T06:14:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.290	-	-
2014-05-12T08:07:00	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.579	-	-
2015-04-14T11:46:00	Tha	Manual testing	2⁶⁶	2⁶⁷		-	-	1.158	-	-
2018-01-07T23:33:16	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	2.316	-	-
2018-01-07T23:33:16	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	4.632	-	-
2021-08-07T06:04:30	SRBase	Manual testing	2⁶⁹	2⁷⁰		-	-	9.265	-	-
2021-08-31T20:13:58	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	18.53	-	-
2021-10-29T20:16:00	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	37.06	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.242 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:	1.242 GHz-days
Estimated T-Level:	0.100

Digits	B1	Complete	FacMiss
20	11000	0.077	92.596%
25	50000	0.007	99.291%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		2	1.242

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-05-03T23:27:02	Bruce	Desk2	50000	5000000						1	0.621
2019-10-20T20:15:34	J.R. Allen	lapacer	50000	5000000						1	0.621

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2001-12-08T00:00:00	Luigi Morelli	v4_computers	7379A86C83E09403	5.272
2004-09-16T00:00:00	Team Prime Rib	v4_computers	7379A86C83E09403	5.272

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 = 600000, B2 = 620747400 (P-1 stage 2)

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

B1 = 600000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

B1 = 155000, B2 = 2286250 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 155000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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