M5325181 Mersenne number exponent details

Residue

Status

L-L

666AB6BE4A5CFC82

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	2⁶⁹	22.4193	66.6667%	1000000	22500000	0.4972	5.5299%	22.9165	68.5100%	5.6068%
PrimeNet	2⁶²	0.1154	62.9032%	22000	550000	0.0116	3.0849%	0.1270	64.0476%	1.1444%
GPU72	2⁶⁶	2.7733	65.1515%	32000	600000	0.0144	2.0281%	2.7877	65.8583%	0.7067%
Difference	+3	+19.6460	+1.5152%	+968000	+21900000	+0.4828	+3.5019%	+20.1288	+2.6517%	+2.6517%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

22.4193

66.6667%

1000000

22500000

0.4972

5.5299%

22.9165

68.5100%

5.6068%

PrimeNet

2⁶²

0.1154

62.9032%

22000

550000

0.0116

3.0849%

0.1270

64.0476%

1.1444%

GPU72

2⁶⁶

2.7733

65.1515%

32000

600000

0.0144

2.0281%

2.7877

65.8583%

0.7067%

Difference

+19.6460

+1.5152%

+968000

+21900000

+0.4828

+3.5019%

+20.1288

+2.6517%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-05-31T00:00:00	rschnell	v4_computers	20000	20000		-		-	-	0.005	-	-	0.264%
2009-11-15T09:04:00	harlee	P4_2600	60000	990000		-		-	-	0.025	-	-	1.813%
2019-06-19T07:51:21	King	FactoringMachine	1000000	22500000	6	-		-	-	0.497	-	-	5.530%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-03-09T00:00:00	Lars Fricke	v4_computers	?	2⁶¹		-	-	0.029	-	-
1998-04-05T00:00:00	ANONYMOUS	v4_computers	?	2⁶²		-	-	0.058	-	-
1998-06-01T00:00:00	ANONYMOUS	v4_computers	?	2⁶²		-	-	0.058	-	-
2009-05-27T04:13:00	GrunwalderGIMP	Manual testing	2⁶²	2⁶³		-	-	0.184	-	-
2014-12-26T11:20:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.369	-	-
2014-12-26T11:20:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.702	-	-
2015-08-16T10:50:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.403	-	-
2016-08-04T12:48:00	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.807	-	-
2018-06-19T09:09:05	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	5.613	-	-
2020-08-31T09:54:53	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	11.23	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.161 GHz-days
Estimated T-Level:	0.450

Digits	B1	Curves	Complete	FacMiss
20	11000	9 / 100	0.090	91.352%
25	50000	9 / 280	0.032	96.831%

New Calculation Method

Total ECM effort:	2.161 GHz-days
Estimated T-Level:	0.450

Digits	B1	Complete	FacMiss
20	11000	0.290	74.802%
25	50000	0.026	97.410%
30	250000	0.002	99.839%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	2.161

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-10-12T00:54:00	Lupo	tower	50000	5000000						3	0.720
2014-12-26T15:24:00	S36049	Wolle5	50000	5000000						3	0.720
2018-02-11T21:38:21	Claude Portenier	Petit-Idiot	50000	5000000						3	0.720

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	ANONYMOUS	v4_computers	666AB6BE4A5CFC82	0.841
2000-08-01T00:00:00	rschnell	v4_computers	666AB6BE4A5CFC82	0.841

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 = 1000000, B2 = 22500000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 60000, B2 = 990000 (P-1 stage 2)

B1 = 60000 (P-1 stage 1)

B1 = 20000 (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