M2316511 Mersenne number exponent details

Residue

Status

L-L

B24CCD0F6ABA0EEA

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	12.8270	67.1642%	5000000	305000000	2.0908	10.2880%	14.9179	70.5423%	3.3782%
PrimeNet	2⁵⁸	0.0166	62.0690%	10000	190000	0.0019	2.9318%	0.0185	63.1810%	1.1121%
GPU72	2⁶²	0.2652	64.5161%	13000	200000	0.0023	1.7815%	0.2675	65.1483%	0.6321%
Difference	+5	+12.5618	+2.6481%	+4987000	+304800000	+2.0886	+8.5066%	+14.6504	+5.3941%	+5.3941%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.8270

67.1642%

5000000

305000000

2.0908

10.2880%

14.9179

70.5423%

3.3782%

PrimeNet

2⁵⁸

0.0166

62.0690%

10000

190000

0.0019

2.9318%

0.0185

63.1810%

1.1121%

GPU72

2⁶²

0.2652

64.5161%

13000

200000

0.0023

1.7815%

0.2675

65.1483%

0.6321%

Difference

+12.5618

+2.6481%

+4987000

+304800000

+2.0886

+8.5066%

+14.6504

+5.3941%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2316511	946003378686458272660944377	27	89.612	204187111282108799108 2² × 11 × 1801 × 11305933 × 227905879	2017-09-02	11305933	227905879	104,118,393	2.2634	2.2717

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2316511

946003378686458272660944377

89.612

204187111282108799108
2² × 11 × 1801 × 11305933 × 227905879

2017-09-02

11305933

227905879

104,118,393

2.2634

2.2717

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.285%
2010-02-19T13:17:00	Bud	annan	500000	10000000		-		-	-	0.100	-	-	4.824%
2018-02-26T11:40:39	alpertron	Manual testing	500000	15000000	12	-		-	-	0.126	-	-	5.214%
2021-04-05T09:19:51	ViliamF	3	5000000	305000000		-		-	-	2.091	-	-	10.288%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:11	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.066	-	-
2009-01-13T02:20:00	Sturle Sunde	othello.ifi	2⁶⁰	2⁶¹		-	-	0.066	-	-
2012-05-24T12:42:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.133	-	-
2013-12-06T02:46:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.424	-	-
2015-03-03T21:35:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.848	-	-
2015-03-03T21:35:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.613	-	-
2015-10-23T09:34:55	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.226	-	-
2017-06-04T00:25:30	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.452	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.657 GHz-days
Estimated T-Level:	1.500

Digits	B1	Curves	Complete	FacMiss
20	11000	30 / 100	0.300	73.970%
25	50000	30 / 280	0.107	89.823%

New Calculation Method

Total ECM effort:	2.657 GHz-days
Estimated T-Level:	1.500

Digits	B1	Complete	FacMiss
20	11000	0.968	37.994%
25	50000	0.087	91.625%
30	250000	0.005	99.463%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		27	2.392
50000	5000000	946003378686458272660944377	3	0.266

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-15T09:06:00	oodaira	Win02	50000	5000000						3	0.266
2010-01-15T16:14:00	BOM	C2Q-2667	50000	5000000						3	0.266
2012-02-02T16:05:00	S36049	Wolle5	50000	5000000						3	0.266
2013-10-07T17:52:00	Bruce	apandya-DESK11	50000	5000000						3	0.266
2015-04-28T12:17:00	dragon325	Falken-i7-920	50000	5000000						3	0.266
2016-02-15T00:06:37	Sintax	cloud2	50000	5000000						3	0.266
2016-04-26T17:45:22	Bruce	Desk6	50000	5000000						3	0.266
2016-08-12T23:09:00	Bruce	Desk6	50000	5000000						3	0.266
2017-01-19T02:22:17	Bruce	Desk6	50000	5000000						3	0.266
2017-09-02T07:59:44	Bruce	Desk6	50000	5000000	946003378686458272660944377	89.612	3	2		3	0.266

date	userid	compid	res64	spent (GHz-days)
1999-03-01T00:00:00	ANONYMOUS	v4_computers	B24CCD0F6ABA0EEA	0.156

date

userid

compid

res64

spent (GHz-days)

1999-03-01T00:00:00

ANONYMOUS

v4_computers

B24CCD0F6ABA0EEA

0.156

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 = 5000000, B2 = 305000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000, B2 = 10000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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