M1116491 Mersenne number exponent details

Residue

Status

L-L

71F1AD087D9B2DED

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	26.6137	68.6567%	5000000	200000000	0.6715	9.0828%	27.2851	71.5036%	2.8468%
PrimeNet	2⁵⁶	0.0086	62.5000%	4500	70000	0.0003	2.0799%	0.0089	63.2800%	0.7800%
GPU72	2⁶⁰	0.1376	65.0000%	4500	22000	0.0002	0.6862%	0.1378	65.2402%	0.2402%
Difference	+7	+26.4761	+3.6567%	+4995500	+199978000	+0.6712	+8.3966%	+27.1473	+6.2634%	+6.2634%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

26.6137

68.6567%

5000000

200000000

0.6715

9.0828%

27.2851

71.5036%

2.8468%

PrimeNet

2⁵⁶

0.0086

62.5000%

4500

70000

0.0003

2.0799%

0.0089

63.2800%

0.7800%

GPU72

2⁶⁰

0.1376

65.0000%

4500

22000

0.0002

0.6862%

0.1378

65.2402%

0.2402%

Difference

+26.4761

+3.6567%

+4995500

+199978000

+0.6712

+8.3966%

+27.1473

+6.2634%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1116491	1249790847808398075335739008807	31	99.980	559695889984065288182233 19 × 79 × 233 × 257 × 461 × 193943 × 69647791	2015-03-11	193943	69647791	1.443e+11	0.1710	0.3046

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1116491

1249790847808398075335739008807

99.980

559695889984065288182233
19 × 79 × 233 × 257 × 461 × 193943 × 69647791

2015-03-11

193943

69647791

1.443e+11

0.1710

0.3046

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-03-10T00:00:00	Jocelyn Larouche	v4_computers	15000	168750		-		-	-	0.001	-	-	0.706%
2012-10-27T09:30:00	kurly	smile	500000	10000000		-		-	-	0.044	-	-	4.411%
2015-03-11T21:09:00	mikr	MSI	5000000	200000000	12		1249790847808398075335739008807	31	99.980	0.671	0.066	1.343	9.083%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-12-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.017	-	-
2003-04-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.034	-	-
2022-03-07T17:30:52	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.103	-	-
2009-02-19T17:25:00	Sturle Sunde	gideon.ifi	2⁶⁰	2⁶¹		-	-	0.138	-	-
2011-05-09T14:44:00	Xyzzy	Manual testing	2⁶¹	2⁶²		-	-	0.275	-	-
2012-10-13T12:00:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.879	-	-
2014-12-22T09:46:00	Matthias Wurtinger	Manual testing	2⁶³	2⁶⁴		-	-	1.758	-	-
2014-12-31T13:39:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	3.347	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.671 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	325 / 100	3.250	3.815%
25	50000	325 / 280	1.161	31.261%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	17.671 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	12.731	0.000%
25	50000	1.349	25.941%
30	250000	0.108	89.793%
35	1000000	0.007	99.295%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	9.91
250000	25000000		44	7.760

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-10-05T03:41:00	Chad Davis	Bayes	50000	5000000						1	0.035
2008-05-20T06:10:00	arnaud	TECH03	50000	5000000						3	0.106
2009-01-08T14:58:00	Sturle Sunde	v21	50000	5000000						3	0.106
2009-05-26T13:50:00	Lukasz Wrobel	WORKER-1	50000	5000000						3	0.106
2009-09-03T20:50:00	Lupo	yorick	50000	5000000						3	0.106
2009-12-07T09:13:00	Lupo	yorick	50000	5000000						3	0.106
2010-05-12T04:38:00	unconnected	can-01	50000	5000000						3	0.106
2011-03-02T14:14:00	James Hintz	nana	50000	5000000						3	0.106
2011-10-17T19:16:00	Andriy Makukha	freehost	50000	5000000						3	0.106
2012-06-19T22:05:00	OS1	Tina	50000	5000000						3	0.106
2012-10-14T16:09:00	OS1	Tina	50000	5000000						3	0.106
2013-06-11T07:50:00	OS1	Tina	50000	5000000						3	0.106
2013-12-12T22:51:00	OS1	Tina	50000	5000000						3	0.106
2014-03-03T08:49:00	Bruce	snowflake	50000	5000000						3	0.106
2014-04-24T02:19:00	OS1	Tina	50000	5000000						3	0.106
2014-12-17T06:16:00	OS1	Tina	50000	5000000						3	0.106
2017-05-26T11:26:43	TJAOI	Manual testing	50000	5000000						94	3.316
2018-03-23T17:16:08	TJAOI	Manual testing	50000	5000000						141	4.973
2020-08-07T11:05:37	TJAOI	Manual testing	250000	25000000						44	7.760

date	userid	compid	res64	spent (GHz-days)
2002-05-05T00:00:00	ANONYMOUS	v4_computers	71F1AD087D9B2DED	0.033

date

userid

compid

res64

spent (GHz-days)

2002-05-05T00:00:00

ANONYMOUS

v4_computers

71F1AD087D9B2DED

0.033

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 = 5000000, B2 = 200000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 500000, B2 = 10000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 15000, B2 = 168750 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

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