M2598919 Mersenne number exponent details

Residue

Status

L-L

A8DB16F4D90B6B2A

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	11.4332	67.1642%	3200000	112000000	0.9180	8.7598%	12.3512	70.0405%	2.8764%
PrimeNet	2⁵⁹	0.0295	62.7119%	11000	200000	0.0021	2.6947%	0.0317	63.7167%	1.0048%
GPU72	2⁶³	0.6141	65.0794%	12000	200000	0.0022	1.5302%	0.6163	65.6137%	0.5344%
Difference	+4	+10.8191	+2.0848%	+3188000	+111800000	+0.9158	+7.2296%	+11.7348	+4.4268%	+4.4268%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

11.4332

67.1642%

3200000

112000000

0.9180

8.7598%

12.3512

70.0405%

2.8764%

PrimeNet

2⁵⁹

0.0295

62.7119%

11000

200000

0.0021

2.6947%

0.0317

63.7167%

1.0048%

GPU72

2⁶³

0.6141

65.0794%

12000

200000

0.0022

1.5302%

0.6163

65.6137%

0.5344%

Difference

+10.8191

+2.0848%

+3188000

+111800000

+0.9158

+7.2296%

+11.7348

+4.4268%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2598919	193797714710036213965549271	27	87.325	37284292952192087165 5 × 7 × 13 × 79 × 1811 × 26557 × 21567011	2016-09-02	26557	21567011	23,663,166	0.1207	0.2207

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2598919

193797714710036213965549271

87.325

37284292952192087165
5 × 7 × 13 × 79 × 1811 × 26557 × 21567011

2016-09-02

26557

21567011

23,663,166

0.1207

0.2207

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-31T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.294%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.913%
2010-11-16T23:08:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.317%
2011-01-15T02:57:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.622%
2011-04-19T05:57:00	James Heinrich	WHS	175000	4156250		-		-	-	0.039	-	-	3.554%
2016-09-03T02:27:52	mikr	MSI	3200000	112000000	12		193797714710036213965549271	27	87.325	0.918	0.361	1.836	8.760%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
2016-02-23T16:29:17	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.030	-	-
2009-01-30T21:58:00	Sturle Sunde	othello.ifi	2⁶⁰	2⁶¹		-	-	0.059	-	-
2012-06-23T13:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.118	-	-
2013-01-14T11:55:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.378	-	-
2015-02-27T20:35:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.755	-	-
2015-02-27T20:35:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.438	-	-
2015-11-05T09:47:20	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.875	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.942 GHz-days
Estimated T-Level:	1.050

Digits	B1	Curves	Complete	FacMiss
20	11000	21 / 100	0.210	80.973%
25	50000	21 / 280	0.075	92.762%

New Calculation Method

Total ECM effort:	1.942 GHz-days
Estimated T-Level:	1.050

Digits	B1	Complete	FacMiss
20	11000	0.677	50.793%
25	50000	0.061	94.061%
30	250000	0.004	99.624%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		21	1.942

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-01T15:47:00	Conductor	home	50000	5000000						3	0.277
2010-06-09T16:43:00	InsDel	fanfare	50000	5000000						3	0.277
2012-11-12T23:26:00	Donna Noble	q8200v2	50000	5000000						3	0.277
2014-08-01T19:43:00	arnaud	SPR05	50000	5000000						3	0.277
2015-10-03T15:45:36	dragon325	Falken-i7-920	50000	5000000						3	0.277
2016-03-20T12:34:16	Jason U	Server7	50000	5000000						3	0.277
2016-08-11T05:32:49	lettp	Home	50000	5000000						3	0.277

date	userid	compid	res64	spent (GHz-days)
1999-08-31T00:00:00	Wayne Beardsley	v4_computers	A8DB16F4D90B6B2A	0.180

date

userid

compid

res64

spent (GHz-days)

1999-08-31T00:00:00

Wayne Beardsley

v4_computers

A8DB16F4D90B6B2A

0.180

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-15T15:10:55

Oliver Kruse

GTX-1

193797714710036213965549271

E311862EA07371__

2017-12-02T09:01:10

kkmrkkblmbrbk

c4.xlarge

193797714710036213965549271

E311862EA07371__

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 = 3200000, B2 = 112000000 (P-1 stage 2)

B1 = 3200000 (P-1 stage 1)

B1 = 175000, B2 = 4156250 (P-1 stage 2)

B1 = 175000 (P-1 stage 1)

B1 = 50000 (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

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