M2023951 Mersenne number exponent details

Residue

Status

L-L

D39EDC795BDFB354

double-checked

PRP

E8636D7E47247422

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	29.4498	69.1176%	4000000	200000000	1.3994	8.7502%	30.8492	71.8199%	2.7023%
PrimeNet	2⁵⁸	0.0190	63.7931%	9000	150000	0.0016	2.6129%	0.0206	64.7392%	0.9461%
GPU72	2⁶²	0.3035	66.1290%	8000	120000	0.0013	1.2738%	0.3049	66.5605%	0.4315%
Difference	+6	+29.1462	+2.9886%	+3992000	+199880000	+1.3981	+7.4764%	+30.5443	+5.2594%	+5.2594%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

29.4498

69.1176%

4000000

200000000

1.3994

8.7502%

30.8492

71.8199%

2.7023%

PrimeNet

2⁵⁸

0.0190

63.7931%

9000

150000

0.0016

2.6129%

0.0206

64.7392%

0.9461%

GPU72

2⁶²

0.3035

66.1290%

8000

120000

0.0013

1.2738%

0.3049

66.5605%

0.4315%

Difference

+29.1462

+2.9886%

+3992000

+199880000

+1.3981

+7.4764%

+30.5443

+5.2594%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2023951	29765948965720026646614889	26	84.622	7353426284954533644 2² × 3 × 7 × 23 × 283 × 13449191750899	2020-12-06	283	13449191750899	3,554,745	69,858	130,476

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2023951

29765948965720026646614889

84.622

7353426284954533644
2² × 3 × 7 × 23 × 283 × 13449191750899

2020-12-06

283

13449191750899

3,554,745

69,858

130,476

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2002-04-28T00:00:00	Jocelyn Larouche	v4_computers	2000	2000		-		-	-	0.000	-	-	0.017%
2003-01-09T00:00:00	ANONYMOUS	v4_computers	25000	412500		-		-	-	0.004	-	-	1.078%
2010-12-11T00:04:00	Jocelyn Larouche	Manual testing	202395	202395		-		-	-	0.019	-	-	1.171%
2013-10-21T08:49:00	David Campeau	i5-2500k	580000	15080000		-		-	-	0.131	-	-	4.746%
2019-03-16T18:47:41	mikr	MSI	4000000	200000000	12	-		-	-	1.399	-	-	8.750%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2002-04-28T00:00:00

Jocelyn Larouche

v4_computers

2000

0.000

-

-

0.017%

2003-01-09T00:00:00

ANONYMOUS

v4_computers

25000

412500

0.004

-

-

1.078%

2010-12-11T00:04:00

Jocelyn Larouche

Manual testing

202395

0.019

-

-

1.171%

2013-10-21T08:49:00

David Campeau

i5-2500k

580000

15080000

0.131

-

-

4.746%

2019-03-16T18:47:41

mikr

MSI

4000000

200000000

1.399

-

-

8.750%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-02T00:00:00	Gavin Brock	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2016-02-23T16:29:03	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.057	-	-
2009-01-02T21:31:00	Sturle Sunde	foster.ifi	2⁶⁰	2⁶¹		-	-	0.076	-	-
2012-02-05T18:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.152	-	-
2013-02-11T20:23:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.485	-	-
2015-04-10T15:56:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.970	-	-
2015-04-10T15:56:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.846	-	-
2015-10-31T16:44:07	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.692	-	-
2016-07-02T13:21:35	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.384	-	-
2019-03-18T03:51:01	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	14.77	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	12.875 GHz-days
Estimated T-Level:	22.714

Digits	B1	Curves	Complete	FacMiss
20	11000	152 / 100	1.520	21.704%
25	50000	152 / 280	0.543	58.052%

New Calculation Method

Total ECM effort:	12.875 GHz-days
Estimated T-Level:	22.714

Digits	B1	Complete	FacMiss
20	11000	5.846	0.289%
25	50000	0.541	58.221%
30	250000	0.034	96.646%
35	1000000	0.002	99.841%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		150	12.71
50000	5000000	29765948965720026646614889	2	0.169

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-02T08:59:00	firehawk	cidnp2	50000	5000000						3	0.254
2009-09-08T06:29:00	StKl	Workstation	50000	5000000						3	0.254
2011-02-15T00:00:00	James Hintz	ryan	50000	5000000						3	0.254
2013-02-12T17:16:00	Xyzzy	J	50000	5000000						3	0.254
2014-03-20T03:05:00	Bruce	snowflake	50000	5000000						3	0.254
2015-07-03T13:22:00	guru	w1	50000	5000000						3	0.254
2015-10-23T19:46:00	mikr	MSI	50000	5000000						12	1.016
2017-05-12T19:50:37	Bruce	Desk6	50000	5000000						3	0.254
2017-11-10T18:33:56	J.R. Allen	lapacer	50000	5000000						3	0.254
2018-03-16T10:31:16	Bruce	Desk6	50000	5000000						3	0.254
2018-08-20T03:55:18	Bruce	Desk6	50000	5000000						3	0.254
2019-11-07T19:52:07	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.254
2019-12-24T13:34:31	mnd9	touchdown	50000	5000000						3	0.254
2019-12-29T20:48:07	TheJudger	myECM	50000	5000000						3	0.254
2020-01-04T07:30:41	daveward2005	MW	50000	5000000						3	0.254
2020-01-10T10:58:23	Alvin Bunk	BADCAT	50000	5000000						3	0.254
2020-01-18T14:53:23	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.254
2020-01-23T19:51:01	mnd9	221Lb	50000	5000000						3	0.254
2020-01-31T14:03:43	IanGlencross	glenx24	50000	5000000						3	0.254
2020-02-10T19:10:41	Corey	Computer	50000	5000000						3	0.254
2020-02-17T02:33:57	mnd9	colab	50000	5000000						3	0.254
2020-02-24T06:58:45	Nesowa	6700T	50000	5000000						3	0.254
2020-03-02T16:14:23	Brett Walker	brain	50000	5000000						3	0.254
2020-03-08T22:19:26	mnd9	colab2	50000	5000000						3	0.254
2020-03-25T08:36:01	Sergey Nosov	TS140-02	50000	5000000						3	0.254
2020-04-05T09:16:19	Yxinity	Olga	50000	5000000						3	0.254
2020-04-06T06:08:48	Keysarecool	HPLaptop	50000	5000000						3	0.254
2020-04-19T23:54:01	mnd9	221Rb	50000	5000000						3	0.254
2020-04-28T05:44:32	mnd9	libproj	50000	5000000						3	0.254
2020-05-08T02:55:02	Leo Custodio	G1-PRIME96-01	50000	5000000						3	0.254
2020-05-21T17:00:44	Leo Custodio	G1-PRIME96-01	50000	5000000						3	0.254
2020-06-24T16:59:18	Dylan Delgado	colab	50000	5000000						3	0.254
2020-06-24T18:54:35	mnd9	75203b	50000	5000000						3	0.254
2020-07-03T09:05:43	Ahmed Azhad	c5.large.az	50000	5000000						3	0.254
2020-07-09T21:11:38	GAN	LMS-02	50000	5000000						3	0.254
2020-07-15T17:54:05	GAN	LMS-13	50000	5000000						3	0.254
2020-07-22T01:28:24	Ahmed Azhad	c5.4xlarge.azf	50000	5000000						3	0.254
2020-07-28T14:12:29	IanGlencross	glenx24	50000	5000000						3	0.254
2020-08-05T01:58:35	daveward2005	Dave2	50000	5000000						3	0.254
2020-08-13T03:01:19	GAN	LMS-11	50000	5000000						3	0.254
2020-09-02T10:48:23	daveward2005	Dave2	50000	5000000						7	0.593
2020-10-07T22:45:49	LaurV	3tits	50000	5000000						7	0.593
2020-11-01T18:47:11	daveward2005	Dave2	50000	5000000						7	0.593
2020-12-06T19:55:11	Zenzoma	AMD3970X	50000	5000000	29765948965720026646614889	84.622	2	2	2600150549109518	2	0.169

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	Gavin Brock	v4_computers	D39EDC795BDFB354	0.133
2016-07-15T14:29:57	Mark Rose	michelangelo	D39EDC795BDFB354	0.133

date

userid

compid

res64

spent (GHz-days)

1999-01-29T00:00:00

Gavin Brock

v4_computers

D39EDC795BDFB354

0.133

2016-07-15T14:29:57

Mark Rose

michelangelo

D39EDC795BDFB354

0.133

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