M1246501 Mersenne number exponent details

Residue

Status

L-L

A5A7140754E00310

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	23.8379	68.6567%	4218475	156083565	0.5741	8.7481%	24.4120	71.3987%	2.7419%
PrimeNet	2⁵⁶	0.0077	62.5000%	5500	90000	0.0005	2.4350%	0.0082	63.4131%	0.9131%
GPU72	2⁶⁰	0.1232	65.0000%	5000	30000	0.0003	0.8331%	0.1235	65.2916%	0.2916%
Difference	+7	+23.7146	+3.6567%	+4213475	+156053565	+0.5738	+7.9150%	+24.2885	+6.1071%	+6.1071%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

23.8379

68.6567%

4218475

156083565

0.5741

8.7481%

24.4120

71.3987%

2.7419%

PrimeNet

2⁵⁶

0.0077

62.5000%

5500

90000

0.0005

2.4350%

0.0082

63.4131%

0.9131%

GPU72

2⁶⁰

0.1232

65.0000%

5000

30000

0.0003

0.8331%

0.1235

65.2916%

0.2916%

Difference

+23.7146

+3.6567%

+4213475

+156053565

+0.5738

+7.9150%

+24.2885

+6.1071%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1246501	11809602372322167394096601	26	83.288	4737101042166098300 2² × 5² × 47371010421660983	2016-05-16	25	47371010421660983	2,986,618	118,610,431	221,531,254

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1246501

11809602372322167394096601

83.288

4737101042166098300
2² × 5² × 47371010421660983

2016-05-16

47371010421660983

2,986,618

118,610,431

221,531,254

	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	-	-	0.238%
2003-11-28T00:00:00	eteo	v4_computers	200000	2000000		-		-	-	0.014	-	-	2.759%
2014-09-25T01:53:00	Jocelyn Larouche	Manual testing	251491	251491		-		-	-	0.012	-	-	1.372%
2015-01-13T07:23:00	mikr	MSI	4218475	156083565		-		-	-	0.574	-	-	8.748%

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

-

-

0.238%

2003-11-28T00:00:00

eteo

v4_computers

200000

2000000

0.014

-

-

2.759%

2014-09-25T01:53:00

Jocelyn Larouche

Manual testing

251491

0.012

-

-

1.372%

2015-01-13T07:23:00

mikr

MSI

4218475

156083565

0.574

-

-

8.748%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.015	-	-
2003-06-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.031	-	-
2016-02-23T16:28:25	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.092	-	-
2009-02-15T11:03:00	Sturle Sunde	goscha.ifi	2⁶⁰	2⁶¹		-	-	0.123	-	-
2012-09-14T15:01:00	Axelsson	Manual testing	2⁶¹	2⁶²		-	-	0.246	-	-
2012-10-07T08:33:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.788	-	-
2015-04-04T11:16:00	omylist	Manual testing	2⁶³	2⁶⁴		-	-	1.575	-	-
2015-04-06T10:49:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	2.997	-	-
2015-09-20T20:58:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	5.995	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.126 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	323 / 100	3.230	3.892%
25	50000	323 / 280	1.154	31.486%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	19.126 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.731	0.000%
25	50000	1.613	19.937%
30	250000	0.131	87.717%
35	1000000	0.009	99.131%

ECM Summary

B1	B2	factor	curves	GHz-days
		11809602372322167394096601	1	0.00000e+0
50000	5000000		279	10.69
250000	25000000		44	8.432

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-11-09T03:02:00	Chad Davis	Bayes	50000	5000000						1	0.038
2008-08-24T13:35:00	Sturle Sunde	v1	50000	5000000						3	0.115
2009-01-31T05:46:00	Sturle Sunde	v21	50000	5000000						3	0.115
2009-07-02T17:53:00	Lukasz Wrobel	WORKER-1	50000	5000000						3	0.115
2009-10-11T13:08:00	James Hintz	jeff4	50000	5000000						3	0.115
2010-03-16T15:32:00	ClknGo Software Corp	cngs1	50000	5000000						3	0.115
2011-01-19T08:22:00	James Hintz	17_051310	50000	5000000						3	0.115
2011-09-19T09:42:00	Huaiyu Wu	eight	50000	5000000						3	0.115
2012-06-20T11:30:00	soldake	athlonx3_435_unlock	50000	5000000						3	0.115
2012-11-15T22:40:00	Salvetay	server5	50000	5000000						3	0.115
2013-08-28T07:40:00	zampel	dufay	50000	5000000						3	0.115
2014-02-03T09:59:00	jim f in mn	asus	50000	5000000						3	0.115
2014-03-09T05:49:00	Bruce	snowflake	50000	5000000						3	0.115
2014-09-08T18:58:00	OS1	Tina	50000	5000000						3	0.115
2015-03-10T22:20:00	Jason U	Dell-Win7	50000	5000000						3	0.115
2015-06-04T00:44:00	arnaud	sgp-11-100	50000	5000000						3	0.115
2015-10-03T01:43:00	Jason U	Dell-Win7	50000	5000000						3	0.115
2016-01-22T15:05:27	Jason U	Dell-Win7	50000	5000000						3	0.115
2016-03-16T13:19:32	raman22feb1988	Chitra	50000	5000000						3	0.115
2016-04-18T13:53:54	raman22feb1988	Alex_Pandian	50000	5000000						3	0.115
2016-05-16T22:59:27	f0rteOC	Fortissimo			11809602372322167394096601	83.288		1		1	-
2017-11-17T15:46:47	TJAOI	Manual testing	50000	5000000						80	3.066
2018-10-05T13:08:09	TJAOI	Manual testing	50000	5000000						141	5.404
2021-03-12T16:32:49	TJAOI	Manual testing	250000	25000000						44	8.432

date	userid	compid	res64	spent (GHz-days)
2015-11-12T20:09:50	MadPoo	Manual testing	A5A7140754E00310	0.040

date

userid

compid

res64

spent (GHz-days)

2015-11-12T20:09:50

MadPoo

Manual testing

A5A7140754E00310

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 = 4218475, B2 = 156083565 (P-1 stage 2)

B1 = 4218475 (P-1 stage 1)

B1 = 200000, B2 = 2000000 (P-1 stage 2)

B1 = 251491 (P-1 stage 1)

B1 = 200000 (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

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

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