M2272631 Mersenne number exponent details

Residue

Status

L-L

CD4ECB6181E64BC3

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	13.0747	67.1642%	500000	15000000	0.1230	5.2023%	13.1977	68.8724%	1.7082%
PrimeNet	2⁵⁸	0.0169	62.0690%	10000	190000	0.0019	2.9216%	0.0188	63.1771%	1.1082%
GPU72	2⁶²	0.2703	64.5161%	12000	190000	0.0021	1.7081%	0.2724	65.1222%	0.6061%
Difference	+5	+12.8043	+2.6481%	+488000	+14810000	+0.1209	+3.4942%	+12.9253	+3.7502%	+3.7502%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.0747

67.1642%

500000

15000000

0.1230

5.2023%

13.1977

68.8724%

1.7082%

PrimeNet

2⁵⁸

0.0169

62.0690%

10000

190000

0.0019

2.9216%

0.0188

63.1771%

1.1082%

GPU72

2⁶²

0.2703

64.5161%

12000

190000

0.0021

1.7081%

0.2724

65.1222%

0.6061%

Difference

+12.8043

+2.6481%

+488000

+14810000

+0.1209

+3.4942%

+12.9253

+3.7502%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2272631	125101600911338285903	21	66.762	27523518096721 67 × 241 × 1704559243	2010-01-02	241	1704559243	9.831	8.8539	16.537

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2272631

125101600911338285903

66.762

27523518096721
67 × 241 × 1704559243

2010-01-02

241

1704559243

9.831

8.8539

16.537

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-04-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.283%
2016-04-30T03:27:09	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.202%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-01-10T16:53:00	Sturle Sunde	graun.ifi	2⁶⁰	2⁶¹		-	-	0.068	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.960 GHz-days
Estimated T-Level:	0.500

Digits	B1	Curves	Complete	FacMiss
20	11000	10 / 100	0.100	90.438%
25	50000	10 / 280	0.036	96.485%

New Calculation Method

Total ECM effort:	0.960 GHz-days
Estimated T-Level:	0.500

Digits	B1	Complete	FacMiss
20	11000	0.407	66.561%
25	50000	0.038	96.280%
30	250000	0.002	99.760%

ECM Summary

B1	B2	factor	curves	GHz-days
		125101600911338285903	1	0.00000e+0
50000	5000000		3	0.258
50000	7000000		7	0.702

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-29T16:52:00	Martti Järvi	SKYNET	50000	5000000						3	0.258
2010-01-02T14:18:00	KAMCOBILL	PC01			125101600911338285903	66.762		1		1	-
2022-08-01T06:58:59	MarkS	desktop-i7	50000	7000000						7	0.702

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-01T00:00:00	ANONYMOUS	v4_computers	EE32741F9DF602__	0.149
1999-07-27T00:00:00	Stephen Wood	v4_computers	CD4ECB6181E64BC3	0.149
1999-10-15T00:00:00	ANONYMOUS	v4_computers	EE32741F9DF602__	0.149

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-11T02:53:51

Oliver Kruse

GTX-1

125101600911338285903

AE93299848B1D7__

2017-11-21T19:39:15

storm5510

HP-Z220-CMT

125101600911338285903

AE93299848B1D7__

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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