M2568361 Mersenne number exponent details

Residue

Status

L-L

0E2D6C039CD7D2E2

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	2⁶⁷	11.5692	67.1642%	3200000	112000000	0.9180	8.7499%	12.4872	70.0373%	2.8731%
PrimeNet	2⁵⁹	0.0299	62.7119%	11000	200000	0.0021	2.6888%	0.0320	63.7145%	1.0026%
GPU72	2⁶³	0.6214	65.0794%	12000	180000	0.0021	1.4801%	0.6235	65.5962%	0.5169%
Difference	+4	+10.9478	+2.0848%	+3188000	+111820000	+0.9159	+7.2697%	+11.8637	+4.4410%	+4.4410%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

11.5692

67.1642%

3200000

112000000

0.9180

8.7499%

12.4872

70.0373%

2.8731%

PrimeNet

2⁵⁹

0.0299

62.7119%

11000

200000

0.0021

2.6888%

0.0320

63.7145%

1.0026%

GPU72

2⁶³

0.6214

65.0794%

12000

180000

0.0021

1.4801%

0.6235

65.5962%

0.5169%

Difference

+10.9478

+2.0848%

+3188000

+111820000

+0.9159

+7.2697%

+11.8637

+4.4410%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2568361	3233043709085396395645975949761	31	101.351	629398224993565233946080 2⁵ × 3² × 5 × 11 × 31 × 1171 × 2939 × 3967 × 93883649	2016-05-31	3967	93883649	7.141e+10	0.5148	0.9608

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2568361

3233043709085396395645975949761

101.351

629398224993565233946080
2⁵ × 3² × 5 × 11 × 31 × 1171 × 2939 × 3967 × 93883649

2016-05-31

3967

93883649

7.141e+10

0.5148

0.9608

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	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.293%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	202500		-		-	-	0.003	-	-	0.891%
2010-12-21T01:09:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.316%
2011-01-03T22:20:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.433%
2011-01-10T23:57:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.621%
2011-04-15T19:11:00	James Heinrich	WHS	175000	4112500		-		-	-	0.039	-	-	3.540%
2016-06-01T02:38:54	mikr	MSI	3200000	112000000	12		3233043709085396395645975949761	31	101.351	0.918	0.356	1.836	8.750%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
2016-02-23T16:29:16	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.030	-	-
2009-01-28T05:11:00	Sturle Sunde	dittersdorf.ifi	2⁶⁰	2⁶¹		-	-	0.060	-	-
2012-06-17T16:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.120	-	-
2013-01-23T08:30:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.382	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.764	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.455	-	-
2015-11-08T21:03:03	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.910	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.662 GHz-days
Estimated T-Level:	0.900

Digits	B1	Curves	Complete	FacMiss
20	11000	18 / 100	0.180	83.451%
25	50000	18 / 280	0.064	93.763%

New Calculation Method

Total ECM effort:	1.662 GHz-days
Estimated T-Level:	0.900

Digits	B1	Complete	FacMiss
20	11000	0.581	55.954%
25	50000	0.052	94.888%
30	250000	0.003	99.677%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		18	1.662

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-17T18:25:00	Aca Arsov	backo6400	50000	5000000						3	0.277
2010-05-14T22:29:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.277
2012-10-17T20:55:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.277
2014-04-24T15:46:00	Andy Incline	Office-PC	50000	5000000						3	0.277
2015-10-27T09:58:53	lopper	i5-4670	50000	5000000						3	0.277
2015-12-07T22:23:22	guru	w1	50000	5000000						3	0.277

date	userid	compid	res64	spent (GHz-days)
1999-05-09T00:00:00	ANONYMOUS	v4_computers	0E2D6C039CD7D2E2	0.178

date

userid

compid

res64

spent (GHz-days)

1999-05-09T00:00:00

ANONYMOUS

v4_computers

0E2D6C039CD7D2E2

0.178

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-15T04:43:38

Oliver Kruse

GTX-3

3233043709085396395645975949761

76C1BC4C4A1D51__

2017-12-01T20:40:58

kkmrkkblmbrbk

c4.xlarge

3233043709085396395645975949761

76C1BC4C4A1D51__

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 = 3200000, B2 = 112000000 (P-1 stage 2)

B1 = 3200000 (P-1 stage 1)

B1 = 175000, B2 = 4112500 (P-1 stage 2)

B1 = 175000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 202500 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

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