M2393263 Mersenne number exponent details

Residue

Status

L-L

F57036BF2E0174BE

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	12.4157	67.1642%	2000000	60000000	0.5055	7.6131%	12.9211	69.6640%	2.4998%
PrimeNet	2⁵⁹	0.0321	62.7119%	10000	170000	0.0018	2.4783%	0.0339	63.6360%	0.9241%
GPU72	2⁶³	0.6669	65.0794%	10000	140000	0.0017	1.2741%	0.6686	65.5243%	0.4449%
Difference	+4	+11.7488	+2.0848%	+1990000	+59860000	+0.5038	+6.3390%	+12.2525	+4.1397%	+4.1397%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.4157

67.1642%

2000000

60000000

0.5055

7.6131%

12.9211

69.6640%

2.4998%

PrimeNet

2⁵⁹

0.0321

62.7119%

10000

170000

0.0018

2.4783%

0.0339

63.6360%

0.9241%

GPU72

2⁶³

0.6669

65.0794%

10000

140000

0.0017

1.2741%

0.6686

65.5243%

0.4449%

Difference

+11.7488

+2.0848%

+1990000

+59860000

+0.5038

+6.3390%

+12.2525

+4.1397%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2393263	419202676952144754583	21	68.506	87579734645157 3 × 29 × 1006663616611	2015-08-10	29	1006663616611	39.812	5,372.5	10,034

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2393263

419202676952144754583

68.506

87579734645157
3 × 29 × 1006663616611

2015-08-10

1006663616611

39.812

5,372.5

10,034

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-21T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.287%
2010-11-08T11:37:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.243%
2010-11-15T22:51:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.311%
2010-12-24T12:17:00	markr	tiny	100000	2075000		-		-	-	0.020	-	-	2.731%
2014-09-16T20:51:00	ANONYMOUS	Manual testing	126819	126819		-		-	-	0.012	-	-	1.075%
2018-09-28T16:25:18	alpertron	Manual testing	2000000	60000000	12	-		-	-	0.505	-	-	7.613%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.032	-	-
2022-03-09T16:37:57	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.064	-	-
2009-01-14T19:11:00	Sturle Sunde	fungo.ifi	2⁶⁰	2⁶¹		-	-	0.064	-	-
2012-06-02T08:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.128	-	-
2013-12-04T21:14:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.410	-	-
2015-03-10T10:44:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.820	-	-
2015-03-10T10:44:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.561	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.246 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:	1.246 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		13	1.157
50000	5000000	419202676952144754583	1	0.089

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-08T17:02:00	Lukasz Wrobel	cm_-_0	50000	5000000						3	0.267
2010-02-19T20:12:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.267
2010-03-10T10:19:00	Bud	annan	50000	5000000						1	0.089
2012-12-10T02:14:00	Donna Noble	Opt6128x4x4	50000	5000000						3	0.267
2014-07-18T06:12:00	Bruce	xps630	50000	5000000						3	0.267
2015-08-10T16:28:00	guru	w1	50000	5000000	419202676952144754583	68.506	1	2		1	0.089

date	userid	compid	res64	spent (GHz-days)
1999-05-30T00:00:00	ANONYMOUS	v4_computers	F57036BF2E0174BE	0.162

date

userid

compid

res64

spent (GHz-days)

1999-05-30T00:00:00

ANONYMOUS

v4_computers

F57036BF2E0174BE

0.162

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 = 2000000, B2 = 60000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 100000, B2 = 2075000 (P-1 stage 2)

B1 = 126819 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

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

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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