M3717409 Mersenne number exponent details

Residue

Status

L-L

8EA2C24B47D8A5F0

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	7.9932	67.1642%	100000	130364850	1.0961	6.0021%	9.0892	69.1350%	1.9708%
PrimeNet	2⁶⁰	0.0413	63.3333%	16000	320000	0.0050	3.0862%	0.0463	64.4649%	1.1316%
GPU72	2⁶⁴	0.9575	65.6250%	22000	450000	0.0069	2.1074%	0.9644	66.3494%	0.7244%
Difference	+3	+7.0357	+1.5392%	+78000	+129914850	+1.0892	+3.8947%	+8.1249	+2.7856%	+2.7856%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

7.9932

67.1642%

100000

130364850

1.0961

6.0021%

9.0892

69.1350%

1.9708%

PrimeNet

2⁶⁰

0.0413

63.3333%

16000

320000

0.0050

3.0862%

0.0463

64.4649%

1.1316%

GPU72

2⁶⁴

0.9575

65.6250%

22000

450000

0.0069

2.1074%

0.9644

66.3494%

0.7244%

Difference

+7.0357

+1.5392%

+78000

+129914850

+1.0892

+3.8947%

+8.1249

+2.7856%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3717409	3013999814946179951153	22	71.352	405389858224664 2³ × 23 × 983 × 43271 × 51797	2009-09-05	43271	51797	186.64	0.0067	0.0134

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3717409

3013999814946179951153

71.352

405389858224664
2³ × 23 × 983 × 43271 × 51797

2009-09-05

43271

51797

186.64

0.0067

0.0134

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-06T10:52:00	Carsten Kossendey	leela	20000	265000		-		-	-	0.005	-	-	1.148%
2022-03-05T05:36:28	Jocelyn Larouche	Manual testing	90000	90000		-	skipped known factor: 3013999814946179951153	-	-	0.014	-	-	0.960%
2022-03-22T11:09:15	Jocelyn Larouche	Manual testing	100000	100000		-	skipped known factor: 3013999814946179951153	-	-	0.015	-	-	1.019%
2022-05-25T14:14:02	Jocelyn Larouche	Manual testing	100000	130364850		-	skipped known factor: 3013999814946179951153	-	-	1.096	-	-	6.002%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-12-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.041	-	-
2009-03-05T16:15:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.041	-	-

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
		3013999814946179951153	1	0.00000e+0

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-09-05T04:19:00	alan145	Bear4			3013999814946179951153	71.352		1		1	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-01-05T00:00:00	ANONYMOUS	v4_computers	8EA2C24B47D8A5F0	0.390
1999-08-16T00:00:00	ANONYMOUS	v4_computers	8EA2C24B47D8A5F0	0.390

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T17:02:28

kkmrkkblmbrbk

Manual testing

3013999814946179951153

40E8AA01AB8AD1__

2017-12-01T16:04:31

Oliver Kruse

GTX-0

3013999814946179951153

40E8AA01AB8AD1__

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 = 100000, B2 = 130364850 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 20000, B2 = 265000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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