M10319503 Mersenne number exponent details

Residue

Status

L-L

E8E680772F738F8E

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	2⁷³	185.3621	67.1233%	300000	18750000	0.6182	3.3453%	185.9803	68.2231%	1.0998%
PrimeNet	2⁶⁴	0.3449	62.5000%	45000	1300000	0.0537	3.7623%	0.3986	63.9109%	1.4109%
GPU72	2⁶⁸	5.7759	64.7059%	70000	1600000	0.0726	2.6598%	5.8486	65.6446%	0.9388%
Difference	+5	+179.5861	+2.4174%	+230000	+17150000	+0.5456	+0.6854%	+180.1317	+2.5785%	+2.5785%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷³

185.3621

67.1233%

300000

18750000

0.6182

3.3453%

185.9803

68.2231%

1.0998%

PrimeNet

2⁶⁴

0.3449

62.5000%

45000

1300000

0.0537

3.7623%

0.3986

63.9109%

1.4109%

GPU72

2⁶⁸

5.7759

64.7059%

70000

1600000

0.0726

2.6598%

5.8486

65.6446%

0.9388%

Difference

+179.5861

+2.4174%

+230000

+17150000

+0.5456

+0.6854%

+180.1317

+2.5785%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-31T00:00:00	Team Prime Rib	v4_computers	50000	387500		-		-	-	0.032	-	-	0.861%
2013-06-10T00:34:00	Nesowa	Outback	125000	2531250		-		-	-	0.121	-	-	1.835%
2021-06-05T19:16:38	Dylan Delgado	laptop-ryzen73700	300000	18750000		-		-	-	0.618	-	-	3.345%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-09-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.345	-	-
2013-09-25T09:16:00	Nesowa	Manual testing	2⁶⁴	2⁶⁵		-	-	0.362	-	-
2015-04-29T08:20:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	0.724	-	-
2015-12-11T23:17:24	VictordeHollander	Manual testing	2⁶⁶	2⁶⁷		-	-	1.448	-	-
2017-09-26T11:35:14	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	2.897	-	-
2017-11-26T23:00:24	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	5.793	-	-
2020-08-03T19:26:29	ViliamF	Manual testing	2⁶⁹	2⁷⁰		-	-	11.59	-	-
2021-04-16T18:15:16	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	23.17	-	-
2021-04-16T18:15:16	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	46.34	-	-
2021-04-17T22:17:44	-Anonymous-	Manual testing	2⁷²	2⁷³		-	-	92.69	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.993 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:	0.993 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	0.993

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-05-14T00:44:00	WileECoyote	Beaker	50000	5000000						1	0.497
2016-09-27T09:21:15	arnaud	snd-15-157	50000	5000000						1	0.497

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2000-07-03T00:00:00	vidmar	v4_computers	E8E680772F738F8E	3.371
2003-11-08T00:00:00	Team Prime Rib	v4_computers	E8E680772F738F8E	3.371

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 = 18750000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 125000, B2 = 2531250 (P-1 stage 2)

B1 = 125000 (P-1 stage 1)

B1 = 50000, B2 = 387500 (P-1 stage 2)

B1 = 50000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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