M2437429 Mersenne number exponent details

Residue

Status

L-L

9A4313E45984FC7D

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	24.4540	67.6471%	3000000	100000000	0.8115	7.8589%	25.2655	70.1896%	2.5426%
PrimeNet	2⁵⁹	0.0315	62.7119%	10000	180000	0.0019	2.5258%	0.0334	63.6537%	0.9418%
GPU72	2⁶³	0.6548	65.0794%	10000	150000	0.0017	1.3062%	0.6565	65.5355%	0.4561%
Difference	+5	+23.7992	+2.5677%	+2990000	+99850000	+0.8098	+6.5526%	+24.6090	+4.6541%	+4.6541%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

24.4540

67.6471%

3000000

100000000

0.8115

7.8589%

25.2655

70.1896%

2.5426%

PrimeNet

2⁵⁹

0.0315

62.7119%

10000

180000

0.0019

2.5258%

0.0334

63.6537%

0.9418%

GPU72

2⁶³

0.6548

65.0794%

10000

150000

0.0017

1.3062%

0.6565

65.5355%

0.4561%

Difference

+23.7992

+2.5677%

+2990000

+99850000

+0.8098

+6.5526%

+24.6090

+4.6541%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2437429	13791595329861631018107742039	29	93.478	2829127603278214671711 3 × 19 × 13049 × 819653 × 4640560259	2020-07-19	819653	4640560259	1.270e+9	24.842	46.256

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2437429

13791595329861631018107742039

93.478

2829127603278214671711
3 × 19 × 13049 × 819653 × 4640560259

2020-07-19

819653

4640560259

1.270e+9

24.842

46.256

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2003-02-09T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.233%
2003-02-24T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.003	-	-	0.477%
2015-12-21T06:40:00	mikr	MSI	3000000	100000000	12	-		-	-	0.812	-	-	7.859%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2003-02-09T00:00:00

ANONYMOUS

v4_computers

2048

204800

0.001

-

-

0.233%

2003-02-24T00:00:00

ANONYMOUS

v4_computers

4096

409600

0.003

-

-

0.477%

2015-12-21T06:40:00

mikr

MSI

3000000

100000000

0.812

-

-

7.859%

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	-	-
2016-02-23T16:29:14	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.032	-	-
2009-01-10T19:29:00	Sturle Sunde	goober.ifi	2⁶⁰	2⁶¹		-	-	0.063	-	-
2012-06-05T22:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.126	-	-
2013-01-23T08:28:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.403	-	-
2015-02-27T20:41:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.805	-	-
2015-02-27T20:41:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.533	-	-
2015-10-25T20:35:01	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.066	-	-
2017-07-08T12:01:26	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.132	-	-
2019-05-27T13:36:56	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.26	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.442 GHz-days
Estimated T-Level:	3.050

Digits	B1	Curves	Complete	FacMiss
20	11000	61 / 100	0.610	54.169%
25	50000	61 / 280	0.218	80.393%

New Calculation Method

Total ECM effort:	5.442 GHz-days
Estimated T-Level:	3.050

Digits	B1	Complete	FacMiss
20	11000	1.968	13.977%
25	50000	0.178	83.707%
30	250000	0.011	98.911%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		60	5.353
50000	5000000	13791595329861631018107742039	1	0.089

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-09T13:12:00	Lukasz Wrobel	UNIX_05	50000	5000000						3	0.268
2010-03-05T18:25:00	James Classen	towerofart	50000	5000000						3	0.268
2012-04-06T18:03:00	Lukasz Wrobel	i-2	50000	5000000						3	0.268
2013-12-23T00:08:00	Andy Incline	Office-PC	50000	5000000						3	0.268
2015-07-05T23:47:00	guru	w1	50000	5000000						3	0.268
2016-02-21T05:02:54	Jason U	Server7	50000	5000000						3	0.268
2016-06-18T14:46:50	Olivier Termolle	KULbook	50000	5000000						3	0.268
2016-10-18T13:37:11	Bruce	Desk6	50000	5000000						3	0.268
2017-04-24T23:02:29	Bruce	Desk6	50000	5000000						3	0.268
2017-11-23T23:34:46	Bruce	Desk6	50000	5000000						3	0.268
2018-05-08T00:53:04	Bruce	Desk6	50000	5000000						3	0.268
2019-05-26T19:36:32	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.268
2020-04-24T20:03:23	mnd9	50871b	50000	5000000						3	0.268
2020-05-11T15:29:58	mnd9	l2lounge	50000	5000000						3	0.268
2020-05-13T16:33:58	nordi	sweet16	50000	5000000						3	0.268
2020-05-29T12:44:43	daveward2005	Davy	50000	5000000						3	0.268
2020-06-17T13:50:05	mnd9	kitchen	50000	5000000						3	0.268
2020-06-29T18:37:52	GAN	LMS-04	50000	5000000						3	0.268
2020-07-06T17:30:30	GAN	LMS-11	50000	5000000						3	0.268
2020-07-14T09:38:22	GAN	KL-SCH02	50000	5000000						3	0.268
2020-07-19T02:14:16	GAN	LMS-07	50000	5000000	13791595329861631018107742039	93.478	1	2	2629648927730404	1	0.089

date	userid	compid	res64	spent (GHz-days)
2000-01-25T00:00:00	ANONYMOUS	v4_computers	9A4313E45984FC7D	0.165

date

userid

compid

res64

spent (GHz-days)

2000-01-25T00:00:00

ANONYMOUS

v4_computers

9A4313E45984FC7D

0.165

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 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 4096, B2 = 409600 (P-1 stage 2)

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

B1 = 4096 (P-1 stage 1)

B1 = 2048 (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