M2358779 Mersenne number exponent details

Residue

Status

L-L

15BAE27D35A89163

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	12.5972	67.1642%	2000000	60000000	0.5055	7.6017%	13.1026	69.6603%	2.4961%
PrimeNet	2⁵⁸	0.0163	62.0690%	11000	200000	0.0021	3.0507%	0.0184	63.2261%	1.1572%
GPU72	2⁶²	0.2605	64.5161%	13000	220000	0.0024	1.8368%	0.2628	65.1679%	0.6518%
Difference	+5	+12.3367	+2.6481%	+1987000	+59780000	+0.5031	+5.7649%	+12.8398	+4.4924%	+4.4924%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.5972

67.1642%

2000000

60000000

0.5055

7.6017%

13.1026

69.6603%

2.4961%

PrimeNet

2⁵⁸

0.0163

62.0690%

11000

200000

0.0021

3.0507%

0.0184

63.2261%

1.1572%

GPU72

2⁶²

0.2605

64.5161%

13000

220000

0.0024

1.8368%

0.2628

65.1679%

0.6518%

Difference

+12.3367

+2.6481%

+1987000

+59780000

+0.5031

+5.7649%

+12.8398

+4.4924%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2358779	14362896626040413982607	23	73.605	3044561746997157 3 × 17 × 1135613 × 52568339	2015-06-13	1135613	52568339	1,284.4	0.3857	0.5240

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2358779

14362896626040413982607

73.605

3044561746997157
3 × 17 × 1135613 × 52568339

2015-06-13

1135613

52568339

1,284.4

0.3857

0.5240

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%
2010-12-22T11:47:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.791%
2011-01-23T11:57:00	Oscar Östlin		90000	1822500		-		-	-	0.018	-	-	2.590%
2014-08-07T10:52:00	Jocelyn Larouche	Manual testing	117211	117211		-		-	-	0.011	-	-	1.026%
2014-10-22T23:53:00	Jocelyn Larouche	Manual testing	144422	144422		-		-	-	0.014	-	-	1.150%
2018-04-27T12:00:19	alpertron	Manual testing	2000000	60000000	12	-	skipped known factor: 14362896626040413982607	-	-	0.505	-	-	7.602%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-01-17T07:30:00	Sturle Sunde	kraus.ifi	2⁶⁰	2⁶¹		-	-	0.065	-	-
2012-05-30T06:42:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.130	-	-
2013-12-04T21:14:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.416	-	-
2015-03-06T11:15:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.832	-	-
2015-03-06T11:15:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.584	-	-

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		12	1.066
50000	5000000	14362896626040413982607	3	0.266

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-27T03:06:00	Never Odd Or Even	T_Quad	50000	5000000						3	0.266
2010-02-08T16:21:00	Csaba Vágó	timigep	50000	5000000						3	0.266
2012-01-02T11:13:00	S36049	Wolle5	50000	5000000						3	0.266
2013-11-01T04:17:00	arnaud	srv-630	50000	5000000						3	0.266
2015-06-13T12:55:00	guru	w6	50000	5000000	14362896626040413982607	73.605	3	2		3	0.266

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	15BAE27D35A89163	0.159

date

userid

compid

res64

spent (GHz-days)

1999-03-15T00:00:00

ANONYMOUS

v4_computers

15BAE27D35A89163

0.159

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-12T13:06:58

Oliver Kruse

GTX-1

406BE8367386F6__

2017-11-24T15:27:16

storm5510

HP-Z220-CMT

14362896626040413982607

406BE8367386F6__

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 = 90000, B2 = 1822500 (P-1 stage 2)

B1 = 144422 (P-1 stage 1)

B1 = 117211 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 75011 (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