M1261963 Mersenne number exponent details

Residue

Status

L-L

3521926B7722437C

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	23.5458	68.6567%	4218475	156083565	0.5741	8.7583%	24.1199	71.4019%	2.7451%
PrimeNet	2⁵⁶	0.0076	62.5000%	5500	90000	0.0005	2.4411%	0.0081	63.4154%	0.9154%
GPU72	2⁶⁰	0.1217	65.0000%	5500	34000	0.0003	0.9081%	0.1220	65.3178%	0.3178%
Difference	+7	+23.4241	+3.6567%	+4212975	+156049565	+0.5738	+7.8502%	+23.9979	+6.0840%	+6.0840%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

23.5458

68.6567%

4218475

156083565

0.5741

8.7583%

24.1199

71.4019%

2.7451%

PrimeNet

2⁵⁶

0.0076

62.5000%

5500

90000

0.0005

2.4411%

0.0081

63.4154%

0.9154%

GPU72

2⁶⁰

0.1217

65.0000%

5500

34000

0.0003

0.9081%

0.1220

65.3178%

0.3178%

Difference

+23.4241

+3.6567%

+4212975

+156049565

+0.5738

+7.8502%

+23.9979

+6.0840%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1261963	1562497500758296835611884802575769	34	110.267	619074212460387838475408868 2² × 3 × 11 × 17 × 23 × 41 × 59 × 97 × 14723 × 652741 × 5319211	2015-02-06	652741	5319211	1.366e+11	0.0417	0.0611

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1261963

1562497500758296835611884802575769

110.267

619074212460387838475408868
2² × 3 × 11 × 17 × 23 × 41 × 59 × 97 × 14723 × 652741 × 5319211

2015-02-06

652741

5319211

1.366e+11

0.0417

0.0611

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-24T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.239%
2003-12-23T00:00:00	eteo	v4_computers	200000	5000000		-		-	-	0.021	-	-	3.419%
2014-09-29T22:04:00	Jocelyn Larouche	Manual testing	250860	250860		-		-	-	0.012	-	-	1.373%
2015-02-06T11:29:00	mikr	MSI	4218475	156083565	12		1562497500758296835611884802575769	34	110.267	0.574	0.080	1.148	8.758%

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	-	-
2003-06-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.030	-	-
2022-03-07T17:32:04	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.091	-	-
2009-02-14T18:24:00	Sturle Sunde	ghini.ifi	2⁶⁰	2⁶¹		-	-	0.122	-	-
2011-05-09T14:41:00	Xyzzy	Manual testing	2⁶¹	2⁶²		-	-	0.243	-	-
2012-10-11T11:56:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.778	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.240 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	19.240 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.263	0.000%
25	50000	1.334	26.337%
30	250000	0.110	89.576%
35	1000000	0.007	99.255%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		251	9.64
250000	25000000		50	9.60

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-11-10T08:40:00	Chad Davis	Bayes	50000	5000000						1	0.038
2008-09-04T22:02:00	Sturle Sunde	v21	50000	5000000						3	0.115
2009-02-04T04:58:00	Sturle Sunde	v21	50000	5000000						3	0.115
2009-07-07T11:17:00	Lukasz Wrobel	WORKER-1	50000	5000000						3	0.115
2009-10-17T11:53:00	SubPrime	c2d0	50000	5000000						3	0.115
2010-03-27T22:21:00	sannerud.com	snap2	50000	5000000						3	0.115
2010-12-27T20:31:00	Donna Noble	PH9550v2	50000	5000000						3	0.115
2011-10-19T23:20:00	Lukasz Wrobel	4_core_L	50000	5000000						3	0.115
2012-07-07T17:53:00	SWL551	THOR	50000	5000000						3	0.115
2012-12-20T01:06:00	ANONYMOUS		50000	5000000						3	0.115
2013-10-07T15:45:00	ANONYMOUS	BOB	50000	5000000						3	0.115
2014-03-01T07:49:00	Bruce	snowflake	50000	5000000						3	0.115
2014-03-13T13:00:00	Bruce	snowflake	50000	5000000						3	0.115
2014-11-06T00:17:00	arnaud	sgp-11-100	50000	5000000						3	0.115
2018-03-09T17:09:43	TJAOI	Manual testing	50000	5000000						211	8.103
2021-04-23T12:17:19	TJAOI	Manual testing	250000	25000000						50	9.60

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 = 5000000 (P-1 stage 2)

B1 = 250860 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

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