M2420569 Mersenne number exponent details

Residue

Status

L-L

F1066295451A9996

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	12.2756	67.1642%	2000000	60000000	0.5055	7.6219%	12.7810	69.6669%	2.5027%
PrimeNet	2⁵⁹	0.0317	62.7119%	10000	180000	0.0019	2.5225%	0.0336	63.6525%	0.9406%
GPU72	2⁶³	0.6594	65.0794%	10000	140000	0.0017	1.2771%	0.6610	65.5253%	0.4460%
Difference	+4	+11.6162	+2.0848%	+1990000	+59860000	+0.5038	+6.3448%	+12.1200	+4.1416%	+4.1416%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.2756

67.1642%

2000000

60000000

0.5055

7.6219%

12.7810

69.6669%

2.5027%

PrimeNet

2⁵⁹

0.0317

62.7119%

10000

180000

0.0019

2.5225%

0.0336

63.6525%

0.9406%

GPU72

2⁶³

0.6594

65.0794%

10000

140000

0.0017

1.2771%

0.6610

65.5253%

0.4460%

Difference

+11.6162

+2.0848%

+1990000

+59860000

+0.5038

+6.3448%

+12.1200

+4.1416%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2420569	62684242486997755310903	23	75.731	12948245327234579 19 × 1279 × 532827674879	2009-02-06	1279	532827674879	4,515.4	2,843.6	5,311.1

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2420569

62684242486997755310903

75.731

12948245327234579
19 × 1279 × 532827674879

2009-02-06

1279

532827674879

4,515.4

2,843.6

5,311.1

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%
2018-09-28T16:59:41	alpertron	Manual testing	2000000	60000000	12	-		-	-	0.505	-	-	7.622%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-07-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.032	-	-
2022-03-09T16:37:59	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.063	-	-
2009-01-12T08:52:00	Sturle Sunde	othello.ifi	2⁶⁰	2⁶¹		-	-	0.063	-	-

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
		62684242486997755310903	1	0.00000e+0

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-06T19:49:00	alan145	Bear4			62684242486997755310903	75.731		1		1	-

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-13T14:48:13

Oliver Kruse

GTX-0

194670CBDD688A__

2017-11-26T22:35:19

ATH

ec2-1xf

62684242486997755310903

194670CBDD688A__

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

10⁹

10¹⁰

10¹¹

10¹²

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