M2872417 Mersenne number exponent details

Residue

Status

L-L

24A4525BAB321A04

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	10.3446	67.1642%	153065	2783000	0.0332	3.2300%	10.3778	68.2248%	1.0606%
PrimeNet	2⁵⁹	0.0267	62.7119%	13000	240000	0.0028	2.9970%	0.0296	63.8294%	1.1175%
GPU72	2⁶³	0.5556	65.0794%	16000	280000	0.0034	1.8698%	0.5590	65.7323%	0.6530%
Difference	+4	+9.7889	+2.0848%	+137065	+2503000	+0.0298	+1.3601%	+9.8187	+2.4924%	+2.4924%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

10.3446

67.1642%

153065

2783000

0.0332

3.2300%

10.3778

68.2248%

1.0606%

PrimeNet

2⁵⁹

0.0267

62.7119%

13000

240000

0.0028

2.9970%

0.0296

63.8294%

1.1175%

GPU72

2⁶³

0.5556

65.0794%

16000

280000

0.0034

1.8698%

0.5590

65.7323%

0.6530%

Difference

+9.7889

+2.0848%

+137065

+2503000

+0.0298

+1.3601%

+9.8187

+2.4924%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2872417	29294220601653654060487	23	74.633	5099228385302979 3³ × 37 × 43 × 118705412047	2016-09-11	43	118705412047	2,554.1	724.30	1,352.8

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2872417

29294220601653654060487

74.633

5099228385302979
3³ × 37 × 43 × 118705412047

2016-09-11

118705412047

2,554.1

724.30

1,352.8

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-28T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.303%
2009-07-03T00:54:00	Carsten Kossendey	leela	15000	161250		-		-	-	0.003	-	-	0.847%
2010-12-23T00:29:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.324%
2011-01-03T22:20:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.444%
2011-01-22T13:10:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.635%
2011-02-05T20:26:00	markr	tiny	115000	2530000		-		-	-	0.028	-	-	3.013%
2016-09-15T03:47:43	Jocelyn Larouche	low 4M	153065	2783000	6	-		-	-	0.033	-	-	3.230%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:23	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.053	-	-
2009-02-13T04:14:00	Sturle Sunde	gorky.ifi	2⁶⁰	2⁶¹		-	-	0.053	-	-
2012-01-27T05:27:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.107	-	-
2013-01-10T10:24:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.342	-	-
2015-04-21T09:21:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.684	-	-
2015-04-21T09:21:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.301	-	-
2016-02-18T12:13:59	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.602	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.465 GHz-days
Estimated T-Level:	0.700

Digits	B1	Curves	Complete	FacMiss
20	11000	14 / 100	0.140	86.875%
25	50000	14 / 280	0.050	95.114%

New Calculation Method

Total ECM effort:	1.465 GHz-days
Estimated T-Level:	0.700

Digits	B1	Complete	FacMiss
20	11000	0.452	63.660%
25	50000	0.041	96.001%
30	250000	0.003	99.749%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.255
50000	5000000	29294220601653654060487	2	0.209

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-23T18:10:00	James Hintz	18_060209	50000	5000000						3	0.314
2010-12-26T08:30:00	unconnected	X3220--xp	50000	5000000						3	0.314
2013-04-24T00:44:00	Donna Noble	q8200v2	50000	5000000						3	0.314
2015-07-13T17:35:00	Adel El-Atawy	MainMTV	50000	5000000						3	0.314
2016-09-11T10:10:02	Bruce	test	50000	5000000	29294220601653654060487	74.633	2	2		2	0.209

date	userid	compid	res64	spent (GHz-days)
1999-05-02T00:00:00	ANONYMOUS	v4_computers	24A4525BAB321A04	0.222

date

userid

compid

res64

spent (GHz-days)

1999-05-02T00:00:00

ANONYMOUS

v4_computers

24A4525BAB321A04

0.222

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-23T05:40:20

Oliver Kruse

GTX-2

29294220601653654060487

ED8D038A15DA7F__

2017-12-08T00:05:29

kkmrkkblmbrbk

c4.xlarge

29294220601653654060487

ED8D038A15DA7F__

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 = 153065, B2 = 2783000 (P-1 stage 2)

B1 = 115000, B2 = 2530000 (P-1 stage 2)

B1 = 153065 (P-1 stage 1)

B1 = 115000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 161250 (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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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