M634181 Mersenne number exponent details

Residue

Status

L-L

4FC9AC10BC6A504B

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	46.8540	70.1493%	2080000	70720000	0.1282	6.8355%	46.9822	72.1897%	2.0404%
PrimeNet	2⁴⁰	0.0000	50.0000%	6000	220000	0.0004	20.6445%	0.0004	60.3222%	10.3222%
GPU72	2⁴⁴	0.0000	54.5455%	11000	400000	0.0007	15.9125%	0.0007	61.7784%	7.2329%
Difference	+23	+46.8540	+15.6038%	+2069000	+70320000	+0.1275	-9.0770%	+46.9815	+10.4113%	+10.4113%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

46.8540

70.1493%

2080000

70720000

0.1282

6.8355%

46.9822

72.1897%

2.0404%

PrimeNet

2⁴⁰

0.0000

50.0000%

6000

220000

0.0004

20.6445%

0.0004

60.3222%

10.3222%

GPU72

2⁴⁴

0.0000

54.5455%

11000

400000

0.0007

15.9125%

0.0007

61.7784%

7.2329%

Difference

+23

+46.8540

+15.6038%

+2069000

+70320000

+0.1275

-9.0770%

+46.9815

+10.4113%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
634181	59698378235428827001849297	26	85.626	47067302738042315208 2³ × 3² × 911 × 2551 × 281292387449	2014-03-30	2551	281292387449	18,581,654	337.65	630.64

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

634181

59698378235428827001849297

85.626

47067302738042315208
2³ × 3² × 911 × 2551 × 281292387449

2014-03-30

2551

281292387449

18,581,654

337.65

630.64

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2000-12-31T00:00:00	Alex Kruppa	v4_computers	2000	40000		-		-	-	8.96776e-5	-	-	0.111%
2001-05-27T00:00:00	Alex Kruppa	v4_computers	100000	4000000		-		-	-	0.007	-	-	2.589%
2002-05-11T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.002	-	-	1.216%
2002-07-06T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.005	-	-	1.833%
2002-10-07T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.009	-	-	2.591%
2003-05-26T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.018	-	-	3.475%
2011-02-01T23:31:00	Jocelyn Larouche	Manual testing	2000000	2000000		-		-	-	0.044	-	-	2.937%
2013-10-26T00:47:00	David Campeau	i5-2500k	2080000	70720000		-		-	-	0.128	-	-	6.835%
2016-03-17T18:50:01	alpertron	Manual testing	1000000	30000000	12	-		-	-	0.057	-	-	5.495%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2000-12-31T00:00:00

Alex Kruppa

v4_computers

2000

40000

8.96776e-5

-

-

0.111%

2001-05-27T00:00:00

Alex Kruppa

v4_computers

100000

4000000

0.007

-

-

2.589%

2002-05-11T00:00:00

ANONYMOUS

v4_computers

16384

1638400

0.002

-

-

1.216%

2002-07-06T00:00:00

ANONYMOUS

v4_computers

32768

3276800

0.005

-

-

1.833%

2002-10-07T00:00:00

ANONYMOUS

v4_computers

65536

6553600

0.009

-

-

2.591%

2003-05-26T00:00:00

ANONYMOUS

v4_computers

131072

13107200

0.018

-

-

3.475%

2011-02-01T23:31:00

Jocelyn Larouche

Manual testing

2000000

0.044

-

-

2.937%

2013-10-26T00:47:00

David Campeau

i5-2500k

2080000

70720000

0.128

-

-

6.835%

2016-03-17T18:50:01

alpertron

Manual testing

1000000

30000000

0.057

-

-

5.495%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2000-01-12T00:00:00	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.002	-	-
2022-03-07T09:01:56	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.004	-	-
2001-04-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.015	-	-
2001-10-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.030	-	-
2003-10-31T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.061	-	-
2008-10-17T05:53:00	Sturle Sunde	buxtehude.ifi	2⁵⁸	2⁵⁹		-	-	0.061	-	-
2008-10-17T17:05:00	Sturle Sunde	buxtehude.ifi	2⁵⁹	2⁶⁰		-	-	0.121	-	-
2011-01-11T10:54:00	Sid & Andy	Toy_Soldier	2⁶⁰	2⁶¹		-	-	0.242	-	-

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2000-01-12T00:00:00

ANONYMOUS

v4_computers

2⁵³

2⁵⁴

0.002

-

-

2022-03-07T09:01:56

LordJulius

Manual testing

2⁵⁴

2⁵⁵

0.004

-

-

2001-04-15T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁶

0.015

-

-

2001-10-25T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁷

0.030

-

-

2003-10-31T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁸

0.061

-

-

2008-10-17T05:53:00

Sturle Sunde

buxtehude.ifi

2⁵⁸

2⁵⁹

0.061

-

-

2008-10-17T17:05:00

Sturle Sunde

buxtehude.ifi

2⁵⁹

2⁶⁰

0.121

-

-

2011-01-11T10:54:00

Sid & Andy

Toy_Soldier

2⁶⁰

2⁶¹

0.242

-

-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.508 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	324 / 100	3.240	3.853%
25	50000	324 / 280	1.157	31.373%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	8.508 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	12.699	0.000%
25	50000	1.346	26.016%
30	250000	0.107	89.809%
35	1000000	0.007	99.296%

ECM Summary

B1	B2	factor	curves	GHz-days
		59698378235428827001849297	1	0.00000e+0
50000	5000000		280	4.764
250000	25000000		44	3.743

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-25T06:55:00	Chad Davis	Bayes	50000	5000000						1	0.017
2007-10-28T06:01:00	ANONYMOUS	minister	50000	5000000						1	0.017
2008-01-22T04:58:00	Team_Bundu	bundu1	50000	5000000						3	0.051
2008-09-14T13:46:00	Sturle Sunde	v21	50000	5000000						3	0.051
2008-11-28T01:02:00	Sturle Sunde	v23	50000	5000000						3	0.051
2009-02-16T22:38:00	Sturle Sunde	v22	50000	5000000						3	0.051
2009-04-03T21:04:00	Sturle Sunde	v22	50000	5000000						3	0.051
2009-07-02T12:25:00	Architects Cubed	m1_48	50000	5000000						3	0.051
2009-07-12T04:38:00	Architects Cubed	m1_65	50000	5000000						3	0.051
2009-08-31T19:06:00	Sturle Sunde	PREUSW40604NL	50000	5000000						3	0.051
2009-09-30T15:41:00	linded	KCPB8P0-NET214	50000	5000000						3	0.051
2009-10-24T19:48:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2009-11-13T04:36:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2009-12-06T04:19:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2009-12-31T04:01:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-01-20T19:17:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-02-04T20:20:00	James Hintz	02_122109	50000	5000000						3	0.051
2010-02-23T19:51:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-03-18T02:28:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-04-08T02:15:00	James Hintz	05_122109	50000	5000000						3	0.051
2010-05-14T02:51:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-06-13T13:34:00	James Hintz	18_051310	50000	5000000						3	0.051
2010-06-27T23:20:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-07-11T04:45:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-07-29T20:32:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-08-25T10:58:00	sannerud.com	Jim2010	50000	5000000						3	0.051
2010-09-12T22:34:00	Sturle Sunde	PRE6S32KN9Z73PR	50000	5000000						3	0.051
2010-10-01T20:56:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-10-18T18:41:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-11-03T18:25:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-11-24T05:31:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2010-12-07T15:46:00	sannerud.com	Jim2010	50000	5000000						3	0.051
2010-12-24T22:25:00	Sturle Sunde	PREFRB439035V	50000	5000000						3	0.051
2011-01-12T17:15:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2011-01-25T13:10:00	Damian Silvestre	PcMa	50000	5000000						3	0.051
2011-02-12T19:47:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2011-02-26T06:27:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2011-03-11T21:39:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2011-03-27T01:56:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2011-04-18T20:05:00	Sturle Sunde	PREFRB439035V	50000	5000000						3	0.051
2011-05-10T20:29:00	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.051
2011-05-28T04:18:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2011-06-15T20:23:00	Sturle Sunde	PRE6S23JYHZD1NR	50000	5000000						3	0.051
2011-07-12T10:26:00	Lukasz Wrobel	w-l	50000	5000000						3	0.051
2011-08-13T17:25:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.051
2011-10-03T05:54:00	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.051
2011-12-04T21:53:00	Sturle Sunde	PRE000AE4EDFF0C	50000	5000000						3	0.051
2012-02-16T14:07:00	Lackó	Iroda_Laci_uj	50000	5000000						3	0.051
2012-03-17T04:22:00	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.051
2012-06-07T07:46:00	Lukasz Wrobel	v7	50000	5000000						3	0.051
2012-08-29T04:10:00	Sturle Sunde	TOR-ST-0035	50000	5000000						3	0.051
2013-02-03T02:22:00	Olli Heikkilä		50000	5000000						3	0.051
2013-09-30T08:19:00	lopper	Surface_staples	50000	5000000						3	0.051
2014-03-25T13:07:00	Lukasz Wrobel	v7	50000	5000000						3	0.051
2014-03-30T14:01:00	Bruce	snowflake			59698378235428827001849297	85.626		1		1	-
2016-04-08T13:19:32	TJAOI	Manual testing	50000	5000000						31	0.527
2016-12-30T15:06:10	TJAOI	Manual testing	50000	5000000						91	1.548
2019-04-26T10:28:53	TJAOI	Manual testing	250000	25000000						44	3.743

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