M2307959 Mersenne number exponent details

Residue

Status

L-L

CF4EF1D402884210

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	12.8745	67.1642%	5000000	315000000	2.1442	10.3289%	15.0188	70.5557%	3.3916%
PrimeNet	2⁵⁸	0.0166	62.0690%	10000	190000	0.0019	2.9299%	0.0186	63.1803%	1.1113%
GPU72	2⁶²	0.2662	64.5161%	12000	200000	0.0022	1.7387%	0.2684	65.1331%	0.6170%
Difference	+5	+12.6084	+2.6481%	+4988000	+314800000	+2.1420	+8.5901%	+14.7504	+5.4227%	+5.4227%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.8745

67.1642%

5000000

315000000

2.1442

10.3289%

15.0188

70.5557%

3.3916%

PrimeNet

2⁵⁸

0.0166

62.0690%

10000

190000

0.0019

2.9299%

0.0186

63.1803%

1.1113%

GPU72

2⁶²

0.2662

64.5161%

12000

200000

0.0022

1.7387%

0.2684

65.1331%

0.6170%

Difference

+12.6084

+2.6481%

+4988000

+314800000

+2.1420

+8.5901%

+14.7504

+5.4227%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2307959	104017649731374211595599	24	76.461	22534553198599761 3 × 11 × 607 × 7211 × 156009421	2017-10-18	7211	156009421	12,173	0.8333	1.5551

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2307959

104017649731374211595599

76.461

22534553198599761
3 × 11 × 607 × 7211 × 156009421

2017-10-18

7211

156009421

12,173

0.8333

1.5551

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	-	-	0.284%
2010-02-16T08:20:00	Bud	annan	500000	10000000		-		-	-	0.100	-	-	4.822%
2018-02-21T02:45:02	alpertron	Manual testing	500000	15000000	12	-		-	-	0.126	-	-	5.212%
2021-04-08T16:10:38	ViliamF	3	5000000	315000000		-	skipped known factor: 104017649731374211595599	-	-	2.144	-	-	10.329%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-02-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.017	-	-
2004-04-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.017	-	-
2016-02-23T16:29:11	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.050	-	-
2009-01-14T18:40:00	Sturle Sunde	gigi.ifi	2⁶⁰	2⁶¹		-	-	0.067	-	-
2012-05-13T15:34:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.133	-	-
2013-01-23T08:24:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.425	-	-
2015-03-03T21:35:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.851	-	-
2015-03-03T21:35:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.619	-	-
2015-10-22T10:17:24	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.238	-	-
2017-05-31T02:32:34	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.476	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.276 GHz-days
Estimated T-Level:	1.850

Digits	B1	Curves	Complete	FacMiss
20	11000	37 / 100	0.370	68.945%
25	50000	37 / 280	0.132	87.601%

New Calculation Method

Total ECM effort:	3.276 GHz-days
Estimated T-Level:	1.850

Digits	B1	Complete	FacMiss
20	11000	1.423	24.097%
25	50000	0.132	87.663%
30	250000	0.008	99.173%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		30	2.656
50000	5000000	104017649731374211595599	7	0.620

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-18T11:36:00	ksims	ZhViZCJBe1505	50000	5000000						3	0.266
2010-01-16T14:22:00	Dr.MOL	Masha	50000	5000000						3	0.266
2011-11-27T20:52:00	S36049	Wolle5	50000	5000000						3	0.266
2013-10-04T01:14:00	Fretard Loic	Glados	50000	5000000						3	0.266
2015-04-15T18:23:00	Jason U	Server7	50000	5000000						3	0.266
2016-02-15T02:47:25	Sintax	cloud	50000	5000000						3	0.266
2016-04-20T17:20:38	Bruce	Desk6	50000	5000000						3	0.266
2016-08-09T00:32:04	Bruce	Desk6	50000	5000000						3	0.266
2017-01-12T16:58:56	Bruce	Desk6	50000	5000000						3	0.266
2017-08-27T09:08:00	Bruce	Desk6	50000	5000000						3	0.266
2017-10-18T07:21:20	Sid & Andy	Hand_In_The_Box	50000	5000000	104017649731374211595599	76.461	7	2		7	0.620

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	CF4EF1D402884210	0.156
2004-04-29T00:00:00	ANONYMOUS	v4_computers	CF4EF1D402884210	0.156

date

userid

compid

res64

spent (GHz-days)

1999-03-15T00:00:00

ANONYMOUS

v4_computers

CF4EF1D402884210

0.156

2004-04-29T00:00:00

ANONYMOUS

v4_computers

CF4EF1D402884210

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 = 315000000 (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

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