M2562323 Mersenne number exponent details

Residue

Status

L-L

6A30A7B160B5FE63

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	11.5965	67.1642%	3200000	112000000	0.9180	8.7479%	12.5145	70.0366%	2.8724%
PrimeNet	2⁵⁹	0.0300	62.7119%	11000	200000	0.0021	2.6876%	0.0321	63.7140%	1.0022%
GPU72	2⁶³	0.6229	65.0794%	12000	180000	0.0021	1.4794%	0.6250	65.5960%	0.5166%
Difference	+4	+10.9736	+2.0848%	+3188000	+111820000	+0.9159	+7.2685%	+11.8895	+4.4406%	+4.4406%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

11.5965

67.1642%

3200000

112000000

0.9180

8.7479%

12.5145

70.0366%

2.8724%

PrimeNet

2⁵⁹

0.0300

62.7119%

11000

200000

0.0021

2.6876%

0.0321

63.7140%

1.0022%

GPU72

2⁶³

0.6229

65.0794%

12000

180000

0.0021

1.4794%

0.6250

65.5960%

0.5166%

Difference

+10.9736

+2.0848%

+3188000

+111820000

+0.9159

+7.2685%

+11.8895

+4.4406%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2562323	1529036184853987369069420327	28	90.305	298369133176025694081 3 × 13 × 23 × 37 × 137 × 2272729 × 28872973	2016-05-04	2272729	28872973	146,596,212	0.3743	0.4652

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2562323

1529036184853987369069420327

90.305

298369133176025694081
3 × 13 × 23 × 37 × 137 × 2272729 × 28872973

2016-05-04

2272729

28872973

146,596,212

0.3743

0.4652

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-23T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.293%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	198750		-		-	-	0.003	-	-	0.885%
2010-12-21T01:09:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.316%
2011-01-03T14:36:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.433%
2011-01-10T23:57:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.620%
2011-04-13T09:13:00	James Heinrich	WHS	175000	4068750		-		-	-	0.039	-	-	3.531%
2016-05-04T16:21:06	mikr	MSI	3200000	112000000	12		1529036184853987369069420327	28	90.305	0.918	0.355	1.836	8.748%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
2016-02-23T16:29:16	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.030	-	-
2009-01-31T21:42:00	Sturle Sunde	gouffy.ifi	2⁶⁰	2⁶¹		-	-	0.060	-	-
2012-06-17T09:42:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.120	-	-
2013-01-14T11:55:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.383	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.766	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.458	-	-
2015-11-08T21:03:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.916	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.661 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:	1.661 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		18	1.661

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-15T12:36:00	oodaira	Win02	50000	5000000						3	0.277
2010-05-12T07:28:00	James Classen	towerofart	50000	5000000						3	0.277
2012-12-13T10:52:00	Brian V.	dxl5420	50000	5000000						3	0.277
2014-04-19T03:41:00	Luis-M-Ferreira	m_1	50000	5000000						3	0.277
2015-08-13T04:54:00	guru	w6	50000	5000000						3	0.277
2016-03-11T11:48:06	Jason U	Server7	50000	5000000						3	0.277

date	userid	compid	res64	spent (GHz-days)
1999-05-09T00:00:00	ANONYMOUS	v4_computers	6A30A7B160B5FE63	0.178

date

userid

compid

res64

spent (GHz-days)

1999-05-09T00:00:00

ANONYMOUS

v4_computers

6A30A7B160B5FE63

0.178

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-15T02:00:32

Oliver Kruse

GTX-0

1529036184853987369069420327

84F5B1EBA38C3D__

2017-12-01T17:52:00

kkmrkkblmbrbk

c4.xlarge

1529036184853987369069420327

84F5B1EBA38C3D__

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 = 4068750 (P-1 stage 2)

B1 = 175000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 198750 (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