M2422873 Mersenne number exponent details

Residue

Status

L-L

6DAE836A09936A52

double-checked

PRP

E71D54E5CABC550C

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	24.6009	67.6471%	1986400	69524000	0.5550	7.1718%	25.1559	69.9673%	2.3203%
PrimeNet	2⁵⁹	0.0317	62.7119%	10000	180000	0.0019	2.5230%	0.0336	63.6526%	0.9408%
GPU72	2⁶³	0.6587	65.0794%	10000	140000	0.0017	1.2773%	0.6604	65.5254%	0.4461%
Difference	+5	+23.9422	+2.5677%	+1976400	+69384000	+0.5533	+5.8944%	+24.4955	+4.4419%	+4.4419%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

24.6009

67.6471%

1986400

69524000

0.5550

7.1718%

25.1559

69.9673%

2.3203%

PrimeNet

2⁵⁹

0.0317

62.7119%

10000

180000

0.0019

2.5230%

0.0336

63.6526%

0.9408%

GPU72

2⁶³

0.6587

65.0794%

10000

140000

0.0017

1.2773%

0.6604

65.5254%

0.4461%

Difference

+23.9422

+2.5677%

+1976400

+69384000

+0.5533

+5.8944%

+24.4955

+4.4419%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2422873	1193897242703623216127	22	70.016	246380483563031 246380483563031	2020-09-10	1	246380483563031	130.90	1,314,905	2,455,877

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2422873

1193897242703623216127

70.016

246380483563031
246380483563031

2020-09-10

246380483563031

130.90

1,314,905

2,455,877

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2003-10-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.233%
2010-11-14T15:37:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.686%
2011-01-24T00:08:00	Oscar Östlin		95000	1923750		-		-	-	0.019	-	-	2.363%
2014-04-16T15:16:00	mikr	MSI	1986400	69524000		-		-	-	0.555	-	-	7.172%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2003-10-08T00:00:00

ANONYMOUS

v4_computers

2048

204800

0.001

-

-

0.233%

2010-11-14T15:37:00

Oscar Östlin

75011

0.007

-

-

0.686%

2011-01-24T00:08:00

Oscar Östlin

95000

1923750

0.019

-

-

2.363%

2014-04-16T15:16:00

mikr

MSI

1986400

69524000

0.555

-

-

7.172%

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	-	-
2016-02-23T16:29:14	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.032	-	-
2009-01-14T04:42:00	Sturle Sunde	ghibu.ifi	2⁶⁰	2⁶¹		-	-	0.063	-	-
2012-06-04T22:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.127	-	-
2013-01-23T08:28:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.405	-	-
2015-02-27T20:40:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.810	-	-
2015-02-27T20:40:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.542	-	-
2015-10-23T09:34:50	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.084	-	-
2017-07-05T06:34:29	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.168	-	-
2019-04-29T13:20:23	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.34	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.220 GHz-days
Estimated T-Level:	4.050

Digits	B1	Curves	Complete	FacMiss
20	11000	81 / 100	0.810	44.305%
25	50000	81 / 280	0.289	74.841%

New Calculation Method

Total ECM effort:	7.220 GHz-days
Estimated T-Level:	4.050

Digits	B1	Complete	FacMiss
20	11000	2.613	7.332%
25	50000	0.236	78.966%
30	250000	0.015	98.556%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		76	6.774
50000	5000000	1193897242703623216127	5	0.446

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-05T17:43:00	ksims	ZhViZCJBe1505	50000	5000000						3	0.267
2010-02-27T07:15:00	James Classen	towerofart	50000	5000000						3	0.267
2012-05-13T21:09:00	Lukasz Wrobel	WORK_lupo	50000	5000000						3	0.267
2013-12-11T13:31:00	Bruce	apandya-DESK11	50000	5000000						3	0.267
2015-07-02T06:03:00	guru	w6	50000	5000000						3	0.267
2016-02-20T16:46:14	Sintax	cloud	50000	5000000						3	0.267
2016-06-07T15:30:00	Jason U	Server7	50000	5000000						3	0.267
2016-10-05T19:05:14	Bruce	Desk6	50000	5000000						3	0.267
2017-04-15T03:46:48	Bruce	Desk6	50000	5000000						3	0.267
2017-11-15T17:02:43	Bruce	Desk6	50000	5000000						3	0.267
2018-04-21T05:17:18	Bruce	Desk6	50000	5000000						3	0.267
2019-03-23T21:59:28	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.267
2020-04-19T07:25:40	mnd9	eileen	50000	5000000						3	0.267
2020-04-27T17:24:16	nordi	sweet16	50000	5000000						3	0.267
2020-05-07T02:56:04	Brett Walker	brain	50000	5000000						3	0.267
2020-05-20T05:18:13	mnd9	50871b	50000	5000000						3	0.267
2020-06-07T05:35:32	daveward2005	Davy	50000	5000000						3	0.267
2020-06-30T23:57:14	Oliver Kruse	Krusen-NAS	50000	5000000						10	0.891
2020-07-17T12:44:18	daveward2005	Dave2	50000	5000000						3	0.267
2020-07-25T00:17:00	GAN	KL-SCH02	50000	5000000						3	0.267
2020-07-30T14:21:35	GAN	OSB-02	50000	5000000						3	0.267
2020-08-07T03:18:57	GAN	LMS-13	50000	5000000						3	0.267
2020-08-15T14:15:41	GAN	LMS-06	50000	5000000						3	0.267
2020-09-10T05:56:54	MarkS	desktop-i7	50000	5000000	1193897242703623216127	70.016	5	2	1417148942255108	5	0.446

date	userid	compid	res64	spent (GHz-days)
1999-04-13T00:00:00	ANONYMOUS	v4_computers	6DAE836A09936A52	0.164
2018-05-20T12:22:08	kkmrkkblmbrbk	old	6DAE836A09936A52	0.164

date

userid

compid

res64

spent (GHz-days)

1999-04-13T00:00:00

ANONYMOUS

v4_computers

6DAE836A09936A52

0.164

2018-05-20T12:22:08

kkmrkkblmbrbk

old

6DAE836A09936A52

0.164

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 = 1986400, B2 = 69524000 (P-1 stage 2)

B1 = 1986400 (P-1 stage 1)

B1 = 95000, B2 = 1923750 (P-1 stage 2)

B1 = 95000 (P-1 stage 1)

B1 = 75011 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10⁰

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10¹

10²

10³

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10¹⁵

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