M1270651 Mersenne number exponent details

Residue

Status

L-L

ABD297C138093581

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	23.3848	68.6567%	2500000	30000000	0.1837	6.4178%	23.5685	70.6683%	2.0116%
PrimeNet	2⁵⁶	0.0076	62.5000%	5500	90000	0.0005	2.4445%	0.0080	63.4167%	0.9167%
GPU72	2⁶⁰	0.1209	65.0000%	5500	36000	0.0003	0.9301%	0.1212	65.3255%	0.3255%
Difference	+7	+23.2639	+3.6567%	+2494500	+29964000	+0.1834	+5.4878%	+23.4473	+5.3428%	+5.3428%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

23.3848

68.6567%

2500000

30000000

0.1837

6.4178%

23.5685

70.6683%

2.0116%

PrimeNet

2⁵⁶

0.0076

62.5000%

5500

90000

0.0005

2.4445%

0.0080

63.4167%

0.9167%

GPU72

2⁶⁰

0.1209

65.0000%

5500

36000

0.0003

0.9301%

0.1212

65.3255%

0.3255%

Difference

+23.2639

+3.6567%

+2494500

+29964000

+0.1834

+5.4878%

+23.4473

+5.3428%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1270651	55728135367835313759823	23	75.561	21928970019240261 3² × 19 × 113 × 163 × 6962353589	2014-03-03	163	6962353589	11,211	17.433	32.560

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1270651

55728135367835313759823

75.561

21928970019240261
3² × 19 × 113 × 163 × 6962353589

2014-03-03

163

6962353589

11,211

17.433

32.560

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2003-02-24T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.239%
2012-11-23T07:05:00	Sergiosi	Manual testing	2500000	30000000		-		-	-	0.184	-	-	6.418%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2003-02-24T00:00:00

ANONYMOUS

v4_computers

2048

204800

0.001

-

-

0.239%

2012-11-23T07:05:00

Sergiosi

Manual testing

2500000

30000000

0.184

-

-

6.418%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-07-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.008	-	-
2001-11-10T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.015	-	-
2003-06-06T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.030	-	-
2003-06-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.030	-	-
2022-03-07T17:32:05	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.091	-	-
2009-02-14T16:08:00	Sturle Sunde	eames.ifi	2⁶⁰	2⁶¹		-	-	0.121	-	-
2012-09-15T01:11:00	Axelsson	Manual testing	2⁶¹	2⁶²		-	-	0.242	-	-
2012-10-13T12:00:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.773	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.145 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	298 / 100	2.980	5.004%
25	50000	298 / 280	1.064	34.432%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	19.145 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	14.084	0.000%
25	50000	1.587	20.458%
30	250000	0.133	87.509%
35	1000000	0.009	99.085%

ECM Summary

B1	B2	factor	curves	GHz-days
		55728135367835313759823	1	0.00000e+0
50000	5000000		248	9.53
250000	25000000		50	9.61

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-11-25T22:52:00	George Woltman	x32-debug	50000	5000000						1	0.038
2007-12-17T23:02:00	George Woltman	x32-debug	50000	5000000						1	0.038
2008-10-17T16:14:00	Sturle Sunde	v23	50000	5000000						3	0.115
2009-03-13T22:58:00	Sturle Sunde	v21	50000	5000000						3	0.115
2009-08-21T17:52:00	Lupo	yorick	50000	5000000						3	0.115
2009-12-06T20:19:00	Lackó	Ilka	50000	5000000						3	0.115
2010-06-17T14:25:00	Charles A. Morris	pulsar	50000	5000000						3	0.115
2011-03-02T12:14:00	fireredd	ont1	50000	5000000						3	0.115
2011-11-28T15:11:00	Andriy Makukha	freehost	50000	5000000						3	0.115
2012-08-06T01:36:00	soldake		50000	5000000						3	0.115
2013-04-04T22:49:00	OS1	Tina	50000	5000000						3	0.115
2013-11-27T22:58:00	OS1	Tina	50000	5000000						3	0.115
2014-03-03T19:24:00	jim f in mn	asus			55728135367835313759823	75.561		1		1	-
2018-01-05T12:42:20	TJAOI	Manual testing	50000	5000000						216	8.304
2021-03-19T18:32:54	TJAOI	Manual testing	250000	25000000						50	9.61

date	userid	compid	res64	spent (GHz-days)
2002-09-07T00:00:00	ANONYMOUS	v4_computers	ABD297C138093581	0.040

date

userid

compid

res64

spent (GHz-days)

2002-09-07T00:00:00

ANONYMOUS

v4_computers

ABD297C138093581

0.040

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 = 2500000, B2 = 30000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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