M2710679 Mersenne number exponent details

Residue

Status

L-L

28512C19B3D57707

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	10.9618	67.1642%	300000	8000000	0.0806	4.4214%	11.0424	68.6160%	1.4518%
PrimeNet	2⁵⁹	0.0283	62.7119%	12000	220000	0.0026	2.8451%	0.0309	63.7727%	1.0609%
GPU72	2⁶³	0.5888	65.0794%	14000	220000	0.0028	1.6625%	0.5916	65.6599%	0.5806%
Difference	+4	+10.3730	+2.0848%	+286000	+7780000	+0.0778	+2.7588%	+10.4508	+2.9560%	+2.9560%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

10.9618

67.1642%

300000

8000000

0.0806

4.4214%

11.0424

68.6160%

1.4518%

PrimeNet

2⁵⁹

0.0283

62.7119%

12000

220000

0.0026

2.8451%

0.0309

63.7727%

1.0609%

GPU72

2⁶³

0.5888

65.0794%

14000

220000

0.0028

1.6625%

0.5916

65.6599%

0.5806%

Difference

+10.3730

+2.0848%

+286000

+7780000

+0.0778

+2.7588%

+10.4508

+2.9560%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2710679	106519499530775348168805113	27	86.461	19648121288204052964 2² × 587 × 1205459 × 6941774377	2017-11-29	1205459	6941774377	11,192,355	42.484	79.110

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2710679

106519499530775348168805113

86.461

19648121288204052964
2² × 587 × 1205459 × 6941774377

2017-11-29

1205459

6941774377

11,192,355

42.484

79.110

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.298%
2003-11-28T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.921%
2010-12-19T21:41:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.320%
2010-12-26T20:13:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.438%
2011-01-18T00:06:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.627%
2011-04-04T14:30:00	James Heinrich	WHS	300000	8000000		-		-	-	0.081	-	-	4.421%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-01-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.028	-	-
2016-02-23T16:29:19	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.028	-	-
2009-01-26T23:16:00	Sturle Sunde	bruckner.ifi	2⁶⁰	2⁶¹		-	-	0.057	-	-
2012-04-25T01:15:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.113	-	-
2013-01-10T10:18:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.362	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.724	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.378	-	-
2016-01-30T15:58:41	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.757	-	-
2017-09-29T00:40:44	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.514	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.591 GHz-days
Estimated T-Level:	1.250

Digits	B1	Curves	Complete	FacMiss
20	11000	25 / 100	0.250	77.782%
25	50000	25 / 280	0.089	91.444%

New Calculation Method

Total ECM effort:	2.591 GHz-days
Estimated T-Level:	1.250

Digits	B1	Complete	FacMiss
20	11000	0.806	44.644%
25	50000	0.073	92.971%
30	250000	0.004	99.552%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		24	2.487
50000	5000000	106519499530775348168805113	1	0.104

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-14T15:35:00	James Hintz	15_061809	50000	5000000						3	0.311
2010-08-16T04:17:00	James Classen	towerofart	50000	5000000						3	0.311
2013-01-24T09:09:00	Sara	Sara	50000	5000000						3	0.311
2015-02-18T19:03:00	Jason U	Server7	50000	5000000						3	0.311
2016-02-04T15:51:27	Bruce	Desk8	50000	5000000						3	0.311
2016-04-30T11:14:24	AnthonyRais	Main	50000	5000000						3	0.311
2016-11-09T04:38:49	Ensigma	vps_sing	50000	5000000						3	0.311
2017-07-15T00:50:09	Bruce	eleven	50000	5000000						3	0.311
2017-11-29T08:01:45	Chang Chia-Tche	ex-ctcpc	50000	5000000	106519499530775348168805113	86.461	1	2		1	0.104

date	userid	compid	res64	spent (GHz-days)
1998-01-16T00:00:00	ANONYMOUS	v4_computers	28512C19B3D57707	0.209
1999-04-13T00:00:00	ANONYMOUS	v4_computers	28512C19B3D57707	0.209

date

userid

compid

res64

spent (GHz-days)

1998-01-16T00:00:00

ANONYMOUS

v4_computers

28512C19B3D57707

0.209

1999-04-13T00:00:00

ANONYMOUS

v4_computers

28512C19B3D57707

0.209

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 = 300000, B2 = 8000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 217500 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (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

10¹⁰

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