M2571937 Mersenne number exponent details

Residue

Status

L-L

B98AA7CB0174C18D

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	11.5531	67.1642%	15000	202500	0.0025	0.8911%	11.5557	67.4568%	0.2926%
PrimeNet	2⁵⁹	0.0299	62.7119%	11000	200000	0.0021	2.6895%	0.0320	63.7147%	1.0029%
GPU72	2⁶³	0.6206	65.0794%	12000	190000	0.0022	1.5043%	0.6227	65.6047%	0.5253%
Difference	+4	+10.9326	+2.0848%	+3000	+12500	+0.0004	-0.6133%	+10.9329	+1.8521%	+1.8521%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

11.5531

67.1642%

15000

202500

0.0025

0.8911%

11.5557

67.4568%

0.2926%

PrimeNet

2⁵⁹

0.0299

62.7119%

11000

200000

0.0021

2.6895%

0.0320

63.7147%

1.0029%

GPU72

2⁶³

0.6206

65.0794%

12000

190000

0.0022

1.5043%

0.6227

65.6047%

0.5253%

Difference

+10.9326

+2.0848%

+3000

+12500

+0.0004

-0.6133%

+10.9329

+1.8521%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2571937	130486533106125082751	21	66.822	25367365745375 5³ × 937 × 216583699	2009-02-18	937	216583699	7.8238	1.1869	2.2166

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2571937

130486533106125082751

66.822

25367365745375
5³ × 937 × 216583699

2009-02-18

937

216583699

7.8238

1.1869

2.2166

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%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.015	-	-
1999-10-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.015	-	-
1999-03-26T00:00:00	Ian Lowman	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
2022-03-11T02:05:01	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.060	-	-
2009-01-30T18:35:00	Sturle Sunde	scarpia.ifi	2⁶⁰	2⁶¹		-	-	0.060	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.277 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:	0.277 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
		130486533106125082751	1	0.00000e+0
50000	5000000		3	0.277

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-18T04:40:00	Aca Arsov	backo6400			130486533106125082751	66.822		1		1	-
2018-11-16T00:06:56	rucio		50000	5000000						3	0.277

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-11-07T00:00:00	ANONYMOUS	v4_computers	B98AA7CB0174C18D	0.178
1999-04-13T00:00:00	Ian Lowman	v4_computers	B98AA7CB0174C18D	0.178
1999-10-29T00:00:00	ANONYMOUS	v4_computers	B98AA7CB0174C18D	0.178

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-15T07:57:38

Oliver Kruse

GTX-0

130486533106125082751

4906E2530E74AF__

2017-12-01T22:11:07

kkmrkkblmbrbk

c4.xlarge

130486533106125082751

4906E2530E74AF__

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

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10¹

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