M2411413 Mersenne number exponent details

Residue

Status

L-L

405147FFB0A8F56F

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	12.3222	67.1642%	2000000	60000000	0.5055	7.6190%	12.8277	69.6659%	2.5018%
PrimeNet	2⁵⁹	0.0318	62.7119%	10000	180000	0.0019	2.5207%	0.0337	63.6518%	0.9399%
GPU72	2⁶³	0.6619	65.0794%	10000	140000	0.0017	1.2761%	0.6635	65.5250%	0.4456%
Difference	+4	+11.6603	+2.0848%	+1990000	+59860000	+0.5038	+6.3429%	+12.1641	+4.1409%	+4.1409%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.3222

67.1642%

2000000

60000000

0.5055

7.6190%

12.8277

69.6659%

2.5018%

PrimeNet

2⁵⁹

0.0318

62.7119%

10000

180000

0.0019

2.5207%

0.0337

63.6518%

0.9399%

GPU72

2⁶³

0.6619

65.0794%

10000

140000

0.0017

1.2761%

0.6635

65.5250%

0.4456%

Difference

+11.6603

+2.0848%

+1990000

+59860000

+0.5038

+6.3429%

+12.1641

+4.1409%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2411413	10516816780928154409	20	63.189	2180633674308 2² × 3 × 46747 × 3887297	2009-02-01	46747	3887297	1.3153	0.0251	0.0387

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2411413

10516816780928154409

63.189

2180633674308
2² × 3 × 46747 × 3887297

2009-02-01

46747

3887297

1.3153

0.0251

0.0387

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.288%
2018-09-28T16:25:40	alpertron	Manual testing	2000000	60000000	12	-	skipped known factor: 10516816780928154409	-	-	0.505	-	-	7.619%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.032	-	-
2022-03-09T16:37:59	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.064	-	-
2009-01-14T23:14:00	Sturle Sunde	gibus.ifi	2⁶⁰	2⁶¹		-	-	0.064	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:

0.000 GHz-days

Digits	B1	Curves	Complete	FacMiss

New Calculation Method

Total ECM effort:

0.000 GHz-days

Digits	B1	Complete	FacMiss

ECM Summary

B1	B2	factor	curves	GHz-days
		10516816780928154409	1	0.00000e+0

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-01T17:38:00	Aca Arsov	backo6400			10516816780928154409	63.189		1		1	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	405147FFB0A8F56F	0.163

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-13T02:57:56

Oliver Kruse

GTX-2

C379EE09BF8F30__

2017-11-26T13:14:16

ATH

ec2-1xf

10516816780928154409

C379EE09BF8F30__

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 = 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

TF factor-bounds graph:

2⁶⁷

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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