M1813321 Mersenne number exponent details

Residue

Status

L-L

9CB19E780B72656E

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	32.8706	69.1176%	1813321	181332100	0.9120	7.9842%	33.7826	71.5833%	2.4657%
PrimeNet	2⁵⁷	0.0106	63.1579%	8000	150000	0.0012	2.8741%	0.0118	64.2168%	1.0589%
GPU72	2⁶¹	0.1694	65.5738%	9000	130000	0.0012	1.5567%	0.1706	66.1097%	0.5359%
Difference	+7	+32.7012	+3.5439%	+1804321	+181202100	+0.9108	+6.4274%	+33.6119	+5.4737%	+5.4737%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

32.8706

69.1176%

1813321

181332100

0.9120

7.9842%

33.7826

71.5833%

2.4657%

PrimeNet

2⁵⁷

0.0106

63.1579%

8000

150000

0.0012

2.8741%

0.0118

64.2168%

1.0589%

GPU72

2⁶¹

0.1694

65.5738%

9000

130000

0.0012

1.5567%

0.1706

66.1097%

0.5359%

Difference

+32.7012

+3.5439%

+1804321

+181202100

+0.9108

+6.4274%

+33.6119

+5.4737%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1813321	55811178719551590553720951	26	85.529	15389216448591173475 3 × 5² × 7 × 19 × 12193429 × 126525409	2020-08-13	12193429	126525409	7,758,531	1.4492	1.9521

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1813321

55811178719551590553720951

85.529

15389216448591173475
3 × 5² × 7 × 19 × 12193429 × 126525409

2020-08-13

12193429

126525409

7,758,531

1.4492

1.9521

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2011-02-07T12:35:00	Carsten Kossendey	leela	100000	1650000		-		-	-	0.015	-	-	2.198%
2014-05-13T21:10:00	Jocelyn Larouche	Manual testing	135396	135396		-		-	-	0.011	-	-	0.924%
2014-09-20T22:31:00	Jocelyn Larouche	Manual testing	170792	170792		-		-	-	0.013	-	-	1.050%
2015-05-19T03:36:00	mikr	MSI	2780000	91760000		-		-	-	0.600	-	-	7.483%
2018-09-21T11:45:47	Jocelyn Larouche	low 4M	1813321	181332100	12	-		-	-	0.912	-	-	7.984%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2011-02-07T12:35:00

Carsten Kossendey

leela

100000

1650000

0.015

-

-

2.198%

2014-05-13T21:10:00

Jocelyn Larouche

Manual testing

135396

0.011

-

-

0.924%

2014-09-20T22:31:00

Jocelyn Larouche

Manual testing

170792

0.013

-

-

1.050%

2015-05-19T03:36:00

mikr

MSI

2780000

91760000

0.600

-

-

7.483%

2018-09-21T11:45:47

Jocelyn Larouche

low 4M

1813321

181332100

0.912

-

-

7.984%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.021	-	-
2016-02-23T16:28:53	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.064	-	-
2010-04-17T14:28:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.085	-	-
2016-02-23T16:28:53	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.169	-	-
2011-01-21T16:10:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.880	-	-
2016-02-23T16:28:53	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.541	-	-
2015-04-22T21:30:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.083	-	-
2015-04-22T21:30:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.061	-	-
2015-09-02T13:37:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.121	-	-
2018-04-02T12:17:07	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.242	-	-
2019-07-01T11:11:05	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	16.48	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.059 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	18.059 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.297	0.025%
25	50000	0.751	47.207%
30	250000	0.046	95.474%
35	1000000	0.002	99.788%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		159	10.97
50000	5000000	55811178719551590553720951	2	0.138
50000	6500000		90	6.950

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-09-18T09:05:00	Scott Kurowski	HomeOffice	50000	5000000						3	0.207
2009-07-15T02:10:00	James Hintz	11_071409	50000	5000000						3	0.207
2010-10-26T18:55:00	Donna Noble	PH2-940-v3-MVB	50000	5000000						3	0.207
2012-04-18T08:45:00	S36049	Wolle5	50000	5000000						3	0.207
2013-07-24T12:11:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-04-08T01:48:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-08-27T01:57:00	mikr	MSI	50000	5000000						12	0.828
2016-05-22T10:04:39	Bruce	DESK3	50000	5000000						3	0.207
2016-08-22T14:34:55	Bruce	DESK3	50000	5000000						3	0.207
2016-11-01T06:58:11	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2017-01-03T03:34:10	Bruce	DESK3	50000	5000000						3	0.207
2017-04-24T00:10:55	ANONYMOUS	Worker	50000	5000000						3	0.207
2017-11-20T00:48:30	Bruce	DESK3	50000	5000000						3	0.207
2018-01-28T15:11:12	Bruce	DESK3	50000	5000000						3	0.207
2019-11-20T13:17:07	Sergey Nosov	TS140-02	50000	5000000						3	0.207
2019-11-22T10:48:08	Dylan Delgado	laptop-i78750	50000	5000000						3	0.207
2019-11-25T01:40:56	mnd9	25836	50000	5000000						3	0.207
2019-11-27T20:53:02	mnd9	50871b	50000	5000000						3	0.207
2019-12-01T10:18:15	Warachwe	1	50000	5000000						3	0.207
2019-12-04T17:24:56	Alvin Bunk	i7-Core	50000	5000000						3	0.207
2019-12-09T00:45:21	J.R. Allen	lapacer	50000	5000000						3	0.207
2019-12-16T03:33:27	Nesowa	entropy_generator_2	50000	5000000						3	0.207
2019-12-19T04:33:19	Nesowa	6700T	50000	5000000						3	0.207
2019-12-25T23:08:39	mnd9	touchdown	50000	5000000						3	0.207
2019-12-31T00:22:16	Nesowa	entropy_generator_2	50000	5000000						3	0.207
2020-01-04T09:15:40	cappy95833	HomePC	50000	5000000						3	0.207
2020-01-10T17:07:49	daveward2005	Davy	50000	5000000						3	0.207
2020-01-18T22:50:35	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.207
2020-01-24T13:11:37	David_McCann	i5	50000	5000000						3	0.207
2020-01-31T22:48:44	EricP	Cannonfodder	50000	5000000						3	0.207
2020-02-10T05:40:48	Keysarecool	HPLaptop	50000	5000000						3	0.207
2020-02-17T08:15:24	Keysarecool	i9	50000	5000000						3	0.207
2020-02-24T15:22:24	mnd9	office2	50000	5000000						3	0.207
2020-03-02T18:47:21	Sergey Nosov	TS140-02	50000	5000000						3	0.207
2020-03-08T21:22:14	mnd9	75211backdoorb	50000	5000000						3	0.207
2020-03-16T12:05:47	mnd9	75201b	50000	5000000						3	0.207
2020-03-25T20:23:03	Alvin Bunk	BADCAT	50000	5000000						3	0.207
2020-04-06T16:50:28	mnd9	eileen	50000	5000000						3	0.207
2020-04-22T00:05:01	nordi	sweet16	50000	5000000						3	0.207
2020-04-29T18:04:23	mnd9	colab2	50000	5000000						3	0.207
2020-05-07T22:59:43	Greg Hogan	azure4	50000	5000000						3	0.207
2020-05-21T19:17:00	volki	home	50000	5000000						3	0.207
2020-06-09T23:39:13	mnd9	50871b	50000	5000000						3	0.207
2020-06-25T10:38:48	Ahmed Azhad	c5.large.az	50000	5000000						3	0.207
2020-07-03T15:49:05	GAN	GAN-HP	50000	5000000						3	0.207
2020-07-15T15:30:01	clww2	hcpu	50000	5000000						3	0.207
2020-07-15T23:41:16	Ahmed Azhad	c5.large.az	50000	5000000						3	0.207
2020-07-22T18:08:44	mnd9	libproj	50000	5000000						3	0.207
2020-07-28T20:00:24	MarkS	desktop-i7	50000	5000000						3	0.207
2020-08-05T11:05:46	daveward2005	Davy	50000	5000000						3	0.207
2020-08-13T15:47:56	daveward2005	MW	50000	5000000	55811178719551590553720951	85.529	2	2		2	0.138
2021-03-05T18:09:06	TJAOI	Manual testing	50000	6500000						90	6.950

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	9CB19E780B72656E	0.098
2015-07-10T01:00:00	MadPoo	Manual testing	9CB19E780B72656E	0.098

date

userid

compid

res64

spent (GHz-days)

1998-12-21T00:00:00

ANONYMOUS

v4_computers

9CB19E780B72656E

0.098

2015-07-10T01:00:00

MadPoo

Manual testing

9CB19E780B72656E

0.098

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