M4096451 Mersenne number exponent details

Residue

Status

L-L

1D99F8DB79522648

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	116.7055	69.0141%	6000000	160000000	2.6025	7.3588%	119.3079	71.2943%	2.2802%
PrimeNet	2⁶¹	0.0750	63.9344%	17000	340000	0.0063	2.8223%	0.0812	64.9523%	1.0179%
GPU72	2⁶⁵	1.7810	66.1538%	22000	400000	0.0077	1.8083%	1.7887	66.7659%	0.6120%
Difference	+6	+114.9245	+2.8602%	+5978000	+159600000	+2.5948	+5.5505%	+117.5193	+4.5284%	+4.5284%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷¹

116.7055

69.0141%

6000000

160000000

2.6025

7.3588%

119.3079

71.2943%

2.2802%

PrimeNet

2⁶¹

0.0750

63.9344%

17000

340000

0.0063

2.8223%

0.0812

64.9523%

1.0179%

GPU72

2⁶⁵

1.7810

66.1538%

22000

400000

0.0077

1.8083%

1.7887

66.7659%

0.6120%

Difference

+114.9245

+2.8602%

+5978000

+159600000

+2.5948

+5.5505%

+117.5193

+4.5284%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-22T19:32:00	Carsten Kossendey	durandal	20000	300000		-		-	-	0.006	-	-	0.662%
2011-07-02T12:06:00	harlee	P4_2600	40000	580000		-		-	-	0.013	-	-	1.023%
2013-07-28T10:07:00	Squeeky_Squirrel	P4_2600	125000	2343750		-		-	-	0.044	-	-	1.984%
2020-09-29T20:25:27	vbcurtis	Manual testing	6000000	160000000	12	-		-	-	2.602	-	-	7.359%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-08-17T01:45:18	ATH	5960X	2500000	177500000	2	7			-	-	2.377

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2021-08-17T01:45:18

ATH

5960X

2500000

177500000

2.377

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-03T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.075	-	-
2010-11-17T19:07:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.075	-	-
2011-05-28T03:15:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.390	-	-
2016-02-23T16:29:48	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.240	-	-
2013-09-01T12:43:00	Jayder	Manual testing	2⁶³	2⁶⁴		-	-	0.479	-	-
2013-10-28T03:13:00	David Campeau	Manual testing	2⁶⁴	2⁶⁵		-	-	0.912	-	-
2015-05-24T21:48:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.824	-	-
2016-10-15T21:43:26	kkmrkkblmbrbk	Manual testing	2⁶⁶	2⁶⁷		-	-	3.648	-	-
2018-11-09T16:54:03	Yxinity	Manual testing	2⁶⁷	2⁶⁸		-	-	7.297	-	-
2021-07-08T15:43:02	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	14.59	-	-
2021-11-30T17:00:06	mikr	Manual testing	2⁶⁹	2⁷⁰		-	-	29.19	-	-
2022-04-19T18:25:22	mikr	Manual testing	2⁷⁰	2⁷¹		-	-	58.37	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.170 GHz-days
Estimated T-Level:	0.600

Digits	B1	Curves	Complete	FacMiss
20	11000	12 / 100	0.120	88.638%
25	50000	12 / 280	0.043	95.797%

New Calculation Method

Total ECM effort:	2.170 GHz-days
Estimated T-Level:	0.600

Digits	B1	Complete	FacMiss
20	11000	0.462	63.031%
25	50000	0.043	95.819%
30	250000	0.003	99.731%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	2.170

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-02-20T20:54:00	Martti Järvi	Fiia	50000	5000000						3	0.543
2012-11-25T04:28:00	Salvetay	server7	50000	5000000						3	0.543
2016-04-06T20:44:40	deo2016	deo2016.home2	50000	5000000						3	0.543
2019-01-08T23:30:50	IanGlencross	glenx24	50000	5000000						3	0.543

date	userid	compid	res64	spent (GHz-days)
1999-09-30T00:00:00	ANONYMOUS	v4_computers	1D99F8DB79522648	0.511

date

userid

compid

res64

spent (GHz-days)

1999-09-30T00:00:00

ANONYMOUS

v4_computers

1D99F8DB79522648

0.511

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 = 6000000, B2 = 160000000 (P-1 stage 2)

B1 = 6000000 (P-1 stage 1)

B1 = 125000, B2 = 2343750 (P-1 stage 2)

B1 = 125000 (P-1 stage 1)

B1 = 40000, B2 = 580000 (P-1 stage 2)

B1 = 40000 (P-1 stage 1)

B1 = 20000, B2 = 300000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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