M2616767 Mersenne number exponent details

Residue

Status

L-L

AD9D125E6EB66763

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	11.3552	67.1642%	2000000	60000000	0.5779	7.6830%	11.9331	69.6870%	2.5228%
PrimeNet	2⁵⁹	0.0293	62.7119%	11000	200000	0.0024	2.6981%	0.0317	63.7179%	1.0061%
GPU72	2⁶³	0.6099	65.0794%	12000	200000	0.0025	1.5323%	0.6124	65.6144%	0.5351%
Difference	+4	+10.7453	+2.0848%	+1988000	+59800000	+0.5754	+6.1507%	+11.3207	+4.0725%	+4.0725%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

11.3552

67.1642%

2000000

60000000

0.5779

7.6830%

11.9331

69.6870%

2.5228%

PrimeNet

2⁵⁹

0.0293

62.7119%

11000

200000

0.0024

2.6981%

0.0317

63.7179%

1.0061%

GPU72

2⁶³

0.6099

65.0794%

12000

200000

0.0025

1.5323%

0.6124

65.6144%

0.5351%

Difference

+10.7453

+2.0848%

+1988000

+59800000

+0.5754

+6.1507%

+11.3207

+4.0725%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2616767	15262322713516530889	20	63.727	2916255576732 2² × 3 × 243021298061	2010-06-12	4	243021298061	1.2160	1,482.8	2,769.5

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2616767

15262322713516530889

63.727

2916255576732
2² × 3 × 243021298061

2010-06-12

243021298061

1.2160

1,482.8

2,769.5

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	-	-	0.295%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.914%
2019-07-04T12:46:25	alpertron	Manual testing	2000000	60000000	12	-		-	-	0.578	-	-	7.683%

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		-	-	0.029	-	-
2022-03-11T04:28:48	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.059	-	-
2009-01-31T22:41:00	Sturle Sunde	gonsha.ifi	2⁶⁰	2⁶¹		-	-	0.059	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.309 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.309 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
		15262322713516530889	1	0.00000e+0
50000	5000000		3	0.309

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-28T08:33:00	alan145	Bear4	50000	5000000						3	0.309
2010-06-12T09:11:00	SubPrime	abd0			15262322713516530889	63.727		1		1	-

date	userid	compid	res64	spent (GHz-days)
1999-04-23T00:00:00	ANONYMOUS	v4_computers	AD9D125E6EB66763	0.202

date

userid

compid

res64

spent (GHz-days)

1999-04-23T00:00:00

ANONYMOUS

v4_computers

AD9D125E6EB66763

0.202

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-17T12:53:03

Oliver Kruse

GTX-3

15262322713516530889

DFA0236CAD490E__

2017-12-02T15:30:41

kkmrkkblmbrbk

c4.xlarge

15262322713516530889

DFA0236CAD490E__

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 = 2000000, B2 = 60000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 15000, B2 = 217500 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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