M3459641 Mersenne number exponent details

Residue

Status

L-L

3F42D7046D5C3355

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	2⁶⁸	17.2286	67.6471%	3459641	3501597330	29.5516	12.7526%	46.7802	71.7729%	4.1258%
PrimeNet	2⁶⁰	0.0444	63.3333%	15000	280000	0.0045	2.9028%	0.0489	64.3977%	1.0644%
GPU72	2⁶⁴	1.0288	65.6250%	19000	340000	0.0056	1.8557%	1.0344	66.2629%	0.6379%
Difference	+4	+16.1998	+2.0221%	+3440641	+3501257330	+29.5460	+10.8969%	+45.7459	+5.5100%	+5.5100%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

17.2286

67.6471%

3459641

3501597330

29.5516

12.7526%

46.7802

71.7729%

4.1258%

PrimeNet

2⁶⁰

0.0444

63.3333%

15000

280000

0.0045

2.9028%

0.0489

64.3977%

1.0644%

GPU72

2⁶⁴

1.0288

65.6250%

19000

340000

0.0056

1.8557%

1.0344

66.2629%

0.6379%

Difference

+16.1998

+2.0221%

+3440641

+3501257330

+29.5460

+10.8969%

+45.7459

+5.5100%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3459641	12439162888577892241	20	63.432	1797753421320 2³ × 3 × 5 × 6449 × 2323039	2009-07-12	6449	2323039	0.5571	0.0202	0.0360

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3459641

12439162888577892241

63.432

1797753421320
2³ × 3 × 5 × 6449 × 2323039

2009-07-12

6449

2323039

0.5571

0.0202

0.0360

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-06T11:08:00	Carsten Kossendey	leela	20000	235000		-		-	-	0.005	-	-	0.938%
2021-03-18T00:24:12	Jocelyn Larouche	Manual testing	345964	3459641	6	-	skipped known factor: 12439162888577892241	-	-	0.079	-	-	3.496%
2021-06-13T12:36:17	Jocelyn Larouche	Manual testing	3459641	3459641		-	skipped known factor: 12439162888577892241	-	-	0.527	-	-	3.933%
2021-08-04T02:33:14	Jocelyn Larouche	Manual testing	3459641	6919282	6	-	skipped known factor: 12439162888577892241	-	-	0.556	-	-	4.809%
2021-12-21T11:44:41	Jocelyn Larouche	Manual testing	3459641	112173600		-	skipped known factor: 12439162888577892241	-	-	1.429	-	-	8.365%
2022-08-15T00:47:01	Jocelyn Larouche	Manual testing	3459641	3501597330		-	skipped known factor: 12439162888577892241	-	-	29.55	-	-	12.753%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-03-21T17:06:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.044	-	-
2022-05-12T17:15:25	LordJulius	Manual testing	2¹	2⁶²		-	-	0.178	-	-
2022-05-12T17:15:25	LordJulius	Manual testing	2⁶²	2⁶³		-	-	0.284	-	-
2022-05-12T17:15:25	LordJulius	Manual testing	2⁶³	2⁶⁴	12439162888577892241	63.432	20	0.096	0.738	0.195
2022-05-12T17:15:25	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	1.080	-	-
2021-02-28T12:18:14	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.160	-	-
2021-03-18T00:24:15	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.320	-	-
2021-06-13T12:36:28	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.640	-	-

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
		12439162888577892241	1	0.00000e+0

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-12T03:43:00	Sid & Andy	RollerBob			12439162888577892241	63.432		1		1	-

date	userid	compid	res64	spent (GHz-days)
1999-07-12T00:00:00	ANONYMOUS	v4_computers	3F42D7046D5C3355	0.363

date

userid

compid

res64

spent (GHz-days)

1999-07-12T00:00:00

ANONYMOUS

v4_computers

3F42D7046D5C3355

0.363

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-07T00:41:02

Oliver Kruse

GTX-0

12439162888577892241

525DA4B9C404B5__

2017-12-16T16:09:24

kkmrkkblmbrbk

c4.xlarge

12439162888577892241

525DA4B9C404B5__

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 = 3459641, B2 = 3501597330 (P-1 stage 2)

B1 = 3459641, B2 = 112173600 (P-1 stage 2)

B1 = 3459641, B2 = 6919282 (P-1 stage 2)

B1 = 3459641 (P-1 stage 1)

B1 = 345964, B2 = 3459641 (P-1 stage 2)

B1 = 345964 (P-1 stage 1)

B1 = 20000, B2 = 235000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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