M2379799 Mersenne number exponent details

Residue

Status

L-L

42E7DF34E28DEE60

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	12.4859	67.1642%	3000000	100000000	0.8115	8.4994%	13.2974	69.9550%	2.7908%
PrimeNet	2⁵⁹	0.0323	62.7119%	10000	170000	0.0018	2.4757%	0.0341	63.6350%	0.9231%
GPU72	2⁶³	0.6707	65.0794%	10000	140000	0.0017	1.2726%	0.6723	65.5238%	0.4444%
Difference	+4	+11.8152	+2.0848%	+2990000	+99860000	+0.8099	+7.2267%	+12.6251	+4.4312%	+4.4312%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.4859

67.1642%

3000000

100000000

0.8115

8.4994%

13.2974

69.9550%

2.7908%

PrimeNet

2⁵⁹

0.0323

62.7119%

10000

170000

0.0018

2.4757%

0.0341

63.6350%

0.9231%

GPU72

2⁶³

0.6707

65.0794%

10000

140000

0.0017

1.2726%

0.6723

65.5238%

0.4444%

Difference

+11.8152

+2.0848%

+2990000

+99860000

+0.8099

+7.2267%

+12.6251

+4.4312%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2379799	10217866969297194271751	23	73.114	2146792012539125 5³ × 7 × 23 × 106672895033	2017-03-19	125	106672895033	1,358.0	569.30	1,063.3

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2379799

10217866969297194271751

73.114

2146792012539125
5³ × 7 × 23 × 106672895033

2017-03-19

125

106672895033

1,358.0

569.30

1,063.3

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%
2010-11-07T21:16:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.243%
2010-11-15T22:51:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.310%
2010-12-27T19:12:00	markr	tiny	100000	2050000		-		-	-	0.020	-	-	2.721%
2014-09-11T21:44:00	Jocelyn Larouche	Manual testing	126970	126970		-		-	-	0.012	-	-	1.074%
2015-10-16T19:38:09	mikr	MSI	3000000	100000000	12	-		-	-	0.812	-	-	8.499%
2018-09-28T16:24:53	alpertron	Manual testing	2000000	60000000	12	-		-	-	0.505	-	-	7.609%

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	-	-
2016-02-23T16:29:13	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.032	-	-
2009-01-14T07:46:00	Sturle Sunde	morovan.ifi	2⁶⁰	2⁶¹		-	-	0.065	-	-
2012-06-01T07:12:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.129	-	-
2013-12-04T21:14:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.412	-	-
2015-03-09T12:35:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.825	-	-
2015-03-09T12:35:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.570	-	-
2015-11-01T21:51:03	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.140	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.401 GHz-days
Estimated T-Level:	1.350

Digits	B1	Curves	Complete	FacMiss
20	11000	27 / 100	0.270	76.234%
25	50000	27 / 280	0.096	90.792%

New Calculation Method

Total ECM effort:	2.401 GHz-days
Estimated T-Level:	1.350

Digits	B1	Complete	FacMiss
20	11000	0.871	41.855%
25	50000	0.079	92.430%
30	250000	0.005	99.516%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		24	2.134
50000	5000000	10217866969297194271751	3	0.267

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-01T03:12:00	ksims	ZhViZCJBe1505	50000	5000000						3	0.267
2010-03-13T04:27:00	KAMCOBILL	PC01	50000	5000000						3	0.267
2012-01-27T09:32:00	S36049	Wolle5	50000	5000000						3	0.267
2013-11-16T06:20:00	Bruce	apandya-DESK11	50000	5000000						3	0.267
2015-06-23T05:38:00	guru	w6	50000	5000000						3	0.267
2016-02-18T15:53:39	Sintax	cloud2	50000	5000000						3	0.267
2016-05-21T11:18:23	Jason U	Server7	50000	5000000						3	0.267
2016-09-10T21:38:54	Bruce	Desk6	50000	5000000						3	0.267
2017-03-19T04:48:59	Bruce	Desk6	50000	5000000	10217866969297194271751	73.114	3	2		3	0.267

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	42E7DF34E28DEE60	0.161

date

userid

compid

res64

spent (GHz-days)

1999-03-15T00:00:00

ANONYMOUS

v4_computers

42E7DF34E28DEE60

0.161

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 = 2050000 (P-1 stage 2)

B1 = 126970 (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)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

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