M5057167 Mersenne number exponent details

Residue

Status

L-L

0D23CEA0B371C4BD

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	5.8756	65.6716%	1500000	45000000	0.7778	7.6717%	6.6534	68.3052%	2.6336%
PrimeNet	2⁶¹	0.0607	62.2951%	22000	500000	0.0097	3.4047%	0.0704	63.5788%	1.2838%
GPU72	2⁶⁵	1.4426	64.6154%	34000	700000	0.0141	2.4206%	1.4568	65.4719%	0.8565%
Difference	+2	+4.4330	+1.0563%	+1466000	+44300000	+0.7637	+5.2511%	+5.1966	+2.8333%	+2.8333%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

5.8756

65.6716%

1500000

45000000

0.7778

7.6717%

6.6534

68.3052%

2.6336%

PrimeNet

2⁶¹

0.0607

62.2951%

22000

500000

0.0097

3.4047%

0.0704

63.5788%

1.2838%

GPU72

2⁶⁵

1.4426

64.6154%

34000

700000

0.0141

2.4206%

1.4568

65.4719%

0.8565%

Difference

+4.4330

+1.0563%

+1466000

+44300000

+0.7637

+5.2511%

+5.1966

+2.8333%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5057167	233328818419010051958927435857	30	97.558	23069123327251211197784 2³ × 20789 × 31307 × 332749 × 13315249	2017-06-25	332749	13315249	6.489e+9	0.2090	0.2723

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5057167

233328818419010051958927435857

97.558

23069123327251211197784
2³ × 20789 × 31307 × 332749 × 13315249

2017-06-25

332749

13315249

6.489e+9

0.2090

0.2723

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2006-01-15T00:00:00	Jocelyn Larouche	v4_computers	50000	50000		-		-	-	0.010	-	-	0.711%
2009-07-30T08:12:00	harlee	P4_2600	60000	1065000		-		-	-	0.023	-	-	2.360%
2017-06-25T14:33:06	mikr	S063	1500000	45000000	12		233328818419010051958927435857	30	97.558	0.778	1.402	1.556	7.672%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:39:07	Mark Rose	Manual testing	2¹	2⁶¹		-	-	0.061	-	-
2008-09-01T22:32:00	Sturle Sunde	lara	2⁶¹	2⁶²		-	-	0.061	-	-
2009-08-08T04:05:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.316	-	-
2016-02-23T16:39:07	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.194	-	-
2014-09-03T01:17:00	kracker	Manual testing	2⁶³	2⁶⁴		-	-	0.388	-	-
2014-09-14T23:38:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	0.739	-	-
2015-08-01T23:20:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.478	-	-
2016-05-21T13:48:29	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.955	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.265 GHz-days
Estimated T-Level:	0.300

Digits	B1	Curves	Complete	FacMiss
20	11000	6 / 100	0.060	94.148%
25	50000	6 / 280	0.021	97.876%

New Calculation Method

Total ECM effort:	1.265 GHz-days
Estimated T-Level:	0.300

Digits	B1	Complete	FacMiss
20	11000	0.194	82.403%
25	50000	0.017	98.266%
30	250000	0.001	99.892%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	1.265

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-07-10T13:33:00	James Hintz	4115	50000	5000000						3	0.632
2014-06-04T04:32:00	driveByUpgrades	Build_4	50000	5000000						3	0.632

date	userid	compid	res64	spent (GHz-days)
2000-05-17T00:00:00	ANONYMOUS	v4_computers	0D23CEA0B371C4BD	0.701

date

userid

compid

res64

spent (GHz-days)

2000-05-17T00:00:00

ANONYMOUS

v4_computers

0D23CEA0B371C4BD

0.701

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:11:53

alpertron

Manual testing

233328818419010051958927435857

91EC4CA04E0CE6__

2018-01-19T03:49:38

kkmrkkblmbrbk

c4.xlarge

233328818419010051958927435857

91EC4CA04E0CE6__

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 = 1500000, B2 = 45000000 (P-1 stage 2)

B1 = 1500000 (P-1 stage 1)

B1 = 60000, B2 = 1065000 (P-1 stage 2)

B1 = 60000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

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