M2457383 Mersenne number exponent details

Residue

Status

L-L

B9FB618DEB45DE7A

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	12.0917	67.1642%	2000000	60000000	0.5190	7.6337%	12.6107	69.6708%	2.5066%
PrimeNet	2⁵⁹	0.0313	62.7119%	10000	180000	0.0019	2.5297%	0.0332	63.6551%	0.9433%
GPU72	2⁶³	0.6495	65.0794%	10000	160000	0.0018	1.3342%	0.6513	65.5453%	0.4659%
Difference	+4	+11.4422	+2.0848%	+1990000	+59840000	+0.5171	+6.2996%	+11.9593	+4.1255%	+4.1255%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.0917

67.1642%

2000000

60000000

0.5190

7.6337%

12.6107

69.6708%

2.5066%

PrimeNet

2⁵⁹

0.0313

62.7119%

10000

180000

0.0019

2.5297%

0.0332

63.6551%

0.9433%

GPU72

2⁶³

0.6495

65.0794%

10000

160000

0.0018

1.3342%

0.6513

65.5453%

0.4659%

Difference

+11.4422

+2.0848%

+1990000

+59840000

+0.5171

+6.2996%

+11.9593

+4.1255%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2457383	31376792338690644913	20	64.766	6384188451432 2³ × 3 × 11 × 24182532013	2010-03-15	11	24182532013	1.7091	132.51	247.49

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2457383

31376792338690644913

64.766

6384188451432
2³ × 3 × 11 × 24182532013

2010-03-15

24182532013

1.7091

132.51

247.49

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.289%
2003-10-31T00:00:00	Team Prime Rib	v4_computers	15000	232500		-		-	-	0.003	-	-	0.921%
2018-09-28T17:00:57	alpertron	Manual testing	2000000	60000000	12	-		-	-	0.519	-	-	7.634%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-08-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.031	-	-
2022-03-10T05:52:56	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.063	-	-
2009-01-10T19:43:00	Sturle Sunde	gibus.ifi	2⁶⁰	2⁶¹		-	-	0.063	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.275 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.275 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
		31376792338690644913	1	0.00000e+0
50000	5000000		3	0.275

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-09T08:51:00	S36049	Wolle3	50000	5000000						3	0.275
2010-03-15T13:11:00	SubPrime	abd0			31376792338690644913	64.766		1		1	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-03-23T00:00:00	ANONYMOUS	v4_computers	B9FB618DEB45DE7A	0.170
1999-09-14T00:00:00	ANONYMOUS	v4_computers	B9FB618DEB45DE7A	0.170

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-13T21:09:30

Oliver Kruse

GTX-2

DF08069D6E7F50__

2017-11-28T23:35:36

kkmrkkblmbrbk

old

31376792338690644913

DF08069D6E7F50__

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 = 15000, B2 = 232500 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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