M1839743 Mersenne number exponent details

Residue

Status

L-L

EB1CD0A75BFDE583

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	32.3985	69.1176%	1839743	183974300	0.9253	8.0234%	33.3238	71.5955%	2.4778%
PrimeNet	2⁵⁷	0.0104	63.1579%	8000	150000	0.0012	2.8820%	0.0117	64.2197%	1.0618%
GPU72	2⁶¹	0.1670	65.5738%	9000	140000	0.0013	1.5963%	0.1682	66.1233%	0.5496%
Difference	+7	+32.2315	+3.5439%	+1830743	+183834300	+0.9240	+6.4271%	+33.1555	+5.4721%	+5.4721%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

32.3985

69.1176%

1839743

183974300

0.9253

8.0234%

33.3238

71.5955%

2.4778%

PrimeNet

2⁵⁷

0.0104

63.1579%

8000

150000

0.0012

2.8820%

0.0117

64.2197%

1.0618%

GPU72

2⁶¹

0.1670

65.5738%

9000

140000

0.0013

1.5963%

0.1682

66.1233%

0.5496%

Difference

+32.2315

+3.5439%

+1830743

+183834300

+0.9240

+6.4271%

+33.1555

+5.4721%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1839743	971717280196909200199664431	27	89.651	264090495302036534505 3 × 5 × 11 × 23 × 108463 × 641592647453	2020-03-11	108463	641592647453	99,785,726	2,749.7	5,135.7

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1839743

971717280196909200199664431

89.651

264090495302036534505
3 × 5 × 11 × 23 × 108463 × 641592647453

2020-03-11

108463

641592647453

99,785,726

2,749.7

5,135.7

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2011-02-10T06:33:00	Carsten Kossendey	leela	100000	1675000		-		-	-	0.015	-	-	2.211%
2014-05-19T21:00:00	Jocelyn Larouche	Manual testing	134888	134888		-		-	-	0.011	-	-	0.925%
2014-09-23T20:52:00	Jocelyn Larouche	Manual testing	169776	169776		-		-	-	0.013	-	-	1.050%
2015-07-07T14:05:00	mikr	MSI	2780000	91760000		-		-	-	0.600	-	-	7.494%
2018-08-09T11:43:51	Jocelyn Larouche	low 4M	1839743	183974300	12	-		-	-	0.925	-	-	8.023%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2011-02-10T06:33:00

Carsten Kossendey

leela

100000

1675000

0.015

-

-

2.211%

2014-05-19T21:00:00

Jocelyn Larouche

Manual testing

134888

0.011

-

-

0.925%

2014-09-23T20:52:00

Jocelyn Larouche

Manual testing

169776

0.013

-

-

1.050%

2015-07-07T14:05:00

mikr

MSI

2780000

91760000

0.600

-

-

7.494%

2018-08-09T11:43:51

Jocelyn Larouche

low 4M

1839743

183974300

0.925

-

-

8.023%

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	-	-
2016-02-23T16:28:54	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.063	-	-
2010-04-23T13:38:00	Architects Cubed	a3_lm	2⁶⁰	2⁶¹		-	-	0.083	-	-
2016-02-23T16:28:54	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.167	-	-
2011-01-21T16:11:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.868	-	-
2016-02-23T16:28:54	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.534	-	-
2015-04-27T03:38:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.067	-	-
2015-04-27T03:38:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.031	-	-
2015-09-05T13:49:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.062	-	-
2018-01-08T13:22:30	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.124	-	-
2019-06-10T09:46:21	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	16.25	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.597 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:	18.597 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.413	0.022%
25	50000	0.762	46.695%
30	250000	0.047	95.405%
35	1000000	0.002	99.784%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		108	7.464
50000	5000000	971717280196909200199664431	1	0.069
50000	6600000		142	11.06

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-10-10T17:49:00	James Heinrich	Q6600	50000	5000000						3	0.207
2009-07-18T06:48:00	James Hintz	17_071509	50000	5000000						3	0.207
2010-11-18T15:18:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.207
2012-06-08T05:31:00	Jacques MOLNE	Crazy_64	50000	5000000						3	0.207
2013-08-30T01:29:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-05-15T05:28:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-11-20T06:41:00	mikr	MSI	50000	5000000						12	0.829
2016-06-02T19:16:26	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2016-09-09T00:14:34	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2016-11-16T05:02:53	Bruce	DESK3	50000	5000000						3	0.207
2017-01-14T17:06:52	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2017-05-19T12:04:09	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2017-12-11T23:24:16	Bruce	DESK3	50000	5000000						3	0.207
2018-02-12T10:01:50	Bruce	DESK3	50000	5000000						3	0.207
2019-11-25T14:38:20	Massimo Cappelli (ik5pwa)	maxlinux_3	50000	5000000						3	0.207
2019-11-26T06:35:20	cappy95833	HomePC	50000	5000000						3	0.207
2019-11-29T00:18:53	Alvin Bunk	i7-Core	50000	5000000						3	0.207
2019-12-13T02:56:28	DRMEDESY	hm02	50000	5000000						3	0.207
2019-12-15T21:34:40	J.R. Allen	lapdell	50000	5000000						3	0.207
2019-12-19T11:29:51	ANONYMOUS	TimeVampireTheFifth	50000	5000000						3	0.207
2019-12-20T20:55:04	daveward2005	Davy	50000	5000000						3	0.207
2019-12-28T05:30:42	mnd9	50871b	50000	5000000						3	0.207
2020-01-01T08:35:25	Brett Walker	brain	50000	5000000						3	0.207
2020-01-06T21:57:12	Yuji HASEGAWA	sx1w7	50000	5000000						3	0.207
2020-01-15T09:44:22	Alvin Bunk	BADCAT	50000	5000000						3	0.207
2020-01-21T05:43:34	mnd9	touchdown	50000	5000000						3	0.207
2020-01-27T10:49:14	J.R. Allen	lapdell	50000	5000000						3	0.207
2020-02-05T08:37:51	Nesowa	entropy_generator_2	50000	5000000						3	0.207
2020-02-12T23:57:28	daveward2005	Davy	50000	5000000						3	0.207
2020-02-20T06:48:50	mnd9	75202	50000	5000000						3	0.207
2020-02-23T18:31:36	mnd9	kitchen	50000	5000000						3	0.207
2020-02-27T05:26:45	mnd9	75202b	50000	5000000						3	0.207
2020-03-04T18:56:00	EricP	Cannonfodder	50000	5000000						3	0.207
2020-03-11T21:59:15	mnd9	25836b	50000	5000000	971717280196909200199664431	89.651	1	2	5380492991924932	1	0.069
2021-06-04T15:56:34	TJAOI	Manual testing	50000	6600000						142	11.06

date	userid	compid	res64	spent (GHz-days)
1999-01-02T00:00:00	Olli Heikkilä	v4_computers	EB1CD0A75BFDE583	0.100
2015-06-27T00:55:00	MadPoo	Manual testing	EB1CD0A75BFDE583	0.100

date

userid

compid

res64

spent (GHz-days)

1999-01-02T00:00:00

Olli Heikkilä

v4_computers

EB1CD0A75BFDE583

0.100

2015-06-27T00:55:00

MadPoo

Manual testing

EB1CD0A75BFDE583

0.100

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