M6439493 Mersenne number exponent details

Residue

Status

L-L

6315795D996A1AD9

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	148.5107	68.0556%	700000	15000000	0.4020	3.7885%	148.9127	69.2658%	1.2102%
PrimeNet	2⁶²	0.0954	62.9032%	28000	650000	0.0168	3.4841%	0.1122	64.1957%	1.2925%
GPU72	2⁶⁶	2.2934	65.1515%	45000	1000000	0.0264	2.5752%	2.3198	66.0489%	0.8974%
Difference	+6	+146.2173	+2.9040%	+655000	+14000000	+0.3756	+1.2133%	+146.5929	+3.2168%	+3.2168%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

148.5107

68.0556%

700000

15000000

0.4020

3.7885%

148.9127

69.2658%

1.2102%

PrimeNet

2⁶²

0.0954

62.9032%

28000

650000

0.0168

3.4841%

0.1122

64.1957%

1.2925%

GPU72

2⁶⁶

2.2934

65.1515%

45000

1000000

0.0264

2.5752%

2.3198

66.0489%

0.8974%

Difference

+146.2173

+2.9040%

+655000

+14000000

+0.3756

+1.2133%

+146.5929

+3.2168%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-02-18T00:00:00	ANONYMOUS	v4_computers	25000	25000		-		-	-	0.007	-	-	0.197%
2011-08-31T08:03:00	markr	tiny	165000	3630000		-		-	-	0.096	-	-	2.219%
2020-04-09T21:45:59	takahashi	vaio	700000	15000000	12	-		-	-	0.402	-	-	3.788%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.095	-	-
2016-02-23T16:39:24	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.152	-	-
2014-08-02T07:16:00	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.305	-	-
2014-08-05T06:50:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.580	-	-
2015-10-24T21:43:21	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.160	-	-
2016-04-03T19:18:39	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.321	-	-
2018-06-06T15:03:39	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	4.642	-	-
2020-05-17T05:08:13	takahashi	Manual testing	2⁶⁸	2⁶⁹		-	-	9.284	-	-
2021-03-02T12:26:34	takahashi	Manual testing	2⁶⁹	2⁷⁰		-	-	18.57	-	-
2021-08-10T15:29:50	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	37.13	-	-
2021-09-25T07:08:38	SRBase	Manual testing	2⁷¹	2⁷²		-	-	74.27	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.710 GHz-days
Estimated T-Level:	0.300

Digits	B1	Curves	Complete	FacMiss
20	11000	6 / 100	0.060	94.148%
25	50000	6 / 280	0.021	97.876%

New Calculation Method

Total ECM effort:	1.710 GHz-days
Estimated T-Level:	0.300

Digits	B1	Complete	FacMiss
20	11000	0.231	79.392%
25	50000	0.021	97.887%
30	250000	0.001	99.865%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	1.710

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2011-12-11T07:30:00	JimBa	Dell	50000	5000000						3	0.855
2016-11-09T23:34:41	fireredd	ont1	50000	5000000						3	0.855

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-01-10T00:00:00	ANONYMOUS	v4_computers	6315795D996A1AD9	1.207
2002-01-08T00:00:00	ANONYMOUS	v4_computers	6315795D996A1AD9	1.207

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 = 700000, B2 = 15000000 (P-1 stage 2)

B1 = 700000 (P-1 stage 1)

B1 = 165000, B2 = 3630000 (P-1 stage 2)

B1 = 165000 (P-1 stage 1)

B1 = 25000 (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