M2185649 Mersenne number exponent details

Residue

Status

L-L

2063195C97B1DD93

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	13.5950	67.1642%	500000	15000000	0.1230	5.1780%	13.7180	68.8644%	1.7002%
PrimeNet	2⁵⁸	0.0176	62.0690%	10000	180000	0.0018	2.8596%	0.0194	63.1537%	1.0847%
GPU72	2⁶²	0.2811	64.5161%	11000	160000	0.0018	1.5696%	0.2829	65.0731%	0.5569%
Difference	+5	+13.3139	+2.6481%	+489000	+14840000	+0.1212	+3.6084%	+13.4351	+3.7913%	+3.7913%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.5950

67.1642%

500000

15000000

0.1230

5.1780%

13.7180

68.8644%

1.7002%

PrimeNet

2⁵⁸

0.0176

62.0690%

10000

180000

0.0018

2.8596%

0.0194

63.1537%

1.0847%

GPU72

2⁶²

0.2811

64.5161%

11000

160000

0.0018

1.5696%

0.2829

65.0731%

0.5569%

Difference

+13.3139

+2.6481%

+489000

+14840000

+0.1212

+3.6084%

+13.4351

+3.7913%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2185649	105104636675117519441	21	66.510	24044262522280 2³ × 5 × 7 × 11 × 13 × 23 × 26108959	2015-12-09	23	26108959	9.0363	0.1356	0.2533

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2185649

105104636675117519441

66.510

24044262522280
2³ × 5 × 7 × 11 × 13 × 23 × 26108959

2015-12-09

26108959

9.0363

0.1356

0.2533

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.280%
2010-11-06T00:22:00	ANONYMOUS	Manual testing	15000	15000		-		-	-	0.001	-	-	0.238%
2010-11-08T22:12:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.418%
2011-01-13T07:23:00	markr	tiny	90000	1620000		-		-	-	0.017	-	-	2.489%
2014-06-26T21:21:00	ANONYMOUS	Manual testing	119366	119366		-		-	-	0.011	-	-	1.022%
2014-10-10T20:28:00	Jocelyn Larouche	Manual testing	148732	148732		-		-	-	0.014	-	-	1.153%
2016-03-27T12:21:39	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.178%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-01-02T07:58:00	Sturle Sunde	gnom.ifi	2⁶⁰	2⁶¹		-	-	0.070	-	-
2009-01-06T19:44:00	Sturle Sunde	gooch.ifi	2⁶¹	2⁶²		-	-	0.141	-	-
2013-01-23T08:20:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.449	-	-
2015-03-25T10:10:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.898	-	-
2015-03-25T10:10:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.710	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.540 GHz-days
Estimated T-Level:	0.900

Digits	B1	Curves	Complete	FacMiss
20	11000	18 / 100	0.180	83.451%
25	50000	18 / 280	0.064	93.763%

New Calculation Method

Total ECM effort:	1.540 GHz-days
Estimated T-Level:	0.900

Digits	B1	Complete	FacMiss
20	11000	0.581	55.954%
25	50000	0.052	94.888%
30	250000	0.003	99.677%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	1.283
50000	5000000	105104636675117519441	3	0.257

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-21T23:08:00	Never Odd Or Even	T_Quad	50000	5000000						3	0.257
2010-02-08T00:13:00	Reaver	Tinka_2010	50000	5000000						3	0.257
2011-09-10T10:14:00	Lukasz Wrobel	WORK_lupo	50000	5000000						3	0.257
2013-05-17T11:54:00	Xyzzy	J	50000	5000000						3	0.257
2015-03-03T22:13:00	Jason U	Server7	50000	5000000						3	0.257
2015-12-09T08:29:49	guru	w1	50000	5000000	105104636675117519441	66.510	3	2		3	0.257

date	userid	compid	res64	spent (GHz-days)
1999-02-14T00:00:00	ANONYMOUS	v4_computers	2063195C97B1DD93	0.144

date

userid

compid

res64

spent (GHz-days)

1999-02-14T00:00:00

ANONYMOUS

v4_computers

2063195C97B1DD93

0.144

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:30:49

alpertron

Manual testing

105104636675117519441

0EFC3495E8A7C9__

2017-10-24T20:32:47

Oliver Kruse

GTX-1

105104636675117519441

0EFC3495E8A7C9__

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 90000, B2 = 1620000 (P-1 stage 2)

B1 = 148732 (P-1 stage 1)

B1 = 119366 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000 (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

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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