M2365243 Mersenne number exponent details

Residue

Status

L-L

8B1B237CF99F844D

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	12.5627	67.1642%	3000000	100000000	0.8115	8.4943%	13.3743	69.9534%	2.7892%
PrimeNet	2⁵⁹	0.0325	62.7119%	10000	170000	0.0018	2.4728%	0.0343	63.6339%	0.9221%
GPU72	2⁶³	0.6748	65.0794%	10000	140000	0.0017	1.2710%	0.6765	65.5232%	0.4438%
Difference	+4	+11.8880	+2.0848%	+2990000	+99860000	+0.8099	+7.2233%	+12.6978	+4.4301%	+4.4301%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.5627

67.1642%

3000000

100000000

0.8115

8.4943%

13.3743

69.9534%

2.7892%

PrimeNet

2⁵⁹

0.0325

62.7119%

10000

170000

0.0018

2.4728%

0.0343

63.6339%

0.9221%

GPU72

2⁶³

0.6748

65.0794%

10000

140000

0.0017

1.2710%

0.6765

65.5232%

0.4438%

Difference

+11.8880

+2.0848%

+2990000

+99860000

+0.8099

+7.2233%

+12.6978

+4.4301%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2365243	574291998267539007231435534313	30	98.858	121402324891678996033692 2² × 3 × 31 × 41 × 241183 × 2974123 × 11096719	2015-09-09	2974123	11096719	5.188e+10	0.3347	0.5929

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2365243

574291998267539007231435534313

98.858

121402324891678996033692
2² × 3 × 31 × 41 × 241183 × 2974123 × 11096719

2015-09-09

2974123

11096719

5.188e+10

0.3347

0.5929

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	-	-	0.286%
2010-11-03T21:25:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.310%
2010-12-30T23:35:00	markr	tiny	100000	2025000		-		-	-	0.020	-	-	2.711%
2014-09-10T00:51:00	Jocelyn Larouche	Manual testing	127136	127136		-		-	-	0.012	-	-	1.074%
2015-09-09T03:42:00	mikr	MSI	3000000	100000000	12		574291998267539007231435534313	30	98.858	0.812	0.320	1.623	8.494%
2018-04-27T11:59:51	alpertron	Manual testing	2000000	60000000	12	-		-	-	0.505	-	-	7.604%

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	-	-
2022-03-09T16:37:53	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.065	-	-
2009-01-14T07:02:00	Sturle Sunde	rodolfo.ifi	2⁶⁰	2⁶¹		-	-	0.065	-	-
2012-05-30T18:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.130	-	-
2013-12-04T21:14:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.415	-	-
2015-03-09T12:35:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.830	-	-
2015-03-09T12:35:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.580	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.332 GHz-days
Estimated T-Level:	0.750

Digits	B1	Curves	Complete	FacMiss
20	11000	15 / 100	0.150	86.006%
25	50000	15 / 280	0.054	94.775%

New Calculation Method

Total ECM effort:	1.332 GHz-days
Estimated T-Level:	0.750

Digits	B1	Complete	FacMiss
20	11000	0.484	61.639%
25	50000	0.044	95.721%
30	250000	0.003	99.731%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	1.332

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-27T08:34:00	Martti Järvi	SKYNET	50000	5000000						3	0.266
2010-02-07T06:38:00	James Hintz	ryan	50000	5000000						3	0.266
2012-01-09T02:51:00	S36049	Wolle5	50000	5000000						3	0.266
2013-11-14T17:59:00	Andy Incline	Office-PC	50000	5000000						3	0.266
2015-06-16T14:52:00	guru	w6	50000	5000000						3	0.266

date	userid	compid	res64	spent (GHz-days)
1999-03-26T00:00:00	ANONYMOUS	v4_computers	8B1B237CF99F844D	0.160

date

userid

compid

res64

spent (GHz-days)

1999-03-26T00:00:00

ANONYMOUS

v4_computers

8B1B237CF99F844D

0.160

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-12T10:58:24

Oliver Kruse

GTX-2

725CC840C18619__

2017-11-24T20:36:04

Gordon Spence

haswell

574291998267539007231435534313

725CC840C18619__

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 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 2000000, B2 = 60000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 2000000 (P-1 stage 1)

B1 = 100000, B2 = 2025000 (P-1 stage 2)

B1 = 127136 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 20000 (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

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