M1783261 Mersenne number exponent details

Residue

Status

L-L

90EC4DEC2774E069

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	33.4247	69.1176%	1783261	196158710	0.9733	8.0467%	34.3980	71.6027%	2.4850%
PrimeNet	2⁵⁷	0.0108	63.1579%	8000	140000	0.0012	2.8125%	0.0120	64.1941%	1.0362%
GPU72	2⁶¹	0.1723	65.5738%	8000	130000	0.0012	1.4922%	0.1734	66.0875%	0.5137%
Difference	+7	+33.2524	+3.5439%	+1775261	+196028710	+0.9722	+6.5545%	+34.2246	+5.5152%	+5.5152%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

33.4247

69.1176%

1783261

196158710

0.9733

8.0467%

34.3980

71.6027%

2.4850%

PrimeNet

2⁵⁷

0.0108

63.1579%

8000

140000

0.0012

2.8125%

0.0120

64.1941%

1.0362%

GPU72

2⁶¹

0.1723

65.5738%

8000

130000

0.0012

1.4922%

0.1734

66.0875%

0.5137%

Difference

+33.2524

+3.5439%

+1775261

+196028710

+0.9722

+6.5545%

+34.2246

+5.5152%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1783261	5493501031901936260553	22	72.218	1540296409752116 2² × 385074102438029	2020-05-11	4	385074102438029	716.94	1,650,331	3,082,359

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1783261

5493501031901936260553

72.218

1540296409752116
2² × 385074102438029

2020-05-11

385074102438029

716.94

1,650,331

3,082,359

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2011-02-07T12:40:00	Carsten Kossendey	leela	95000	1615000		-		-	-	0.014	-	-	2.158%
2014-04-10T20:52:00	ANONYMOUS	Manual testing	100000	100000		-		-	-	0.008	-	-	0.772%
2014-05-09T20:32:00	Jocelyn Larouche	Manual testing	135993	135993		-		-	-	0.011	-	-	0.924%
2014-09-19T20:39:00	Jocelyn Larouche	Manual testing	171986	171986		-		-	-	0.014	-	-	1.051%
2015-06-01T09:50:00	mikr	MSI	2475400	86660000		-		-	-	0.556	-	-	7.333%
2018-07-02T12:39:36	Jocelyn Larouche	low 4M	1783261	178326100	12	-		-	-	0.897	-	-	7.939%
2018-10-19T12:14:54	Jocelyn Larouche	low 4M	1783261	196158710	12	-		-	-	0.973	-	-	8.047%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2011-02-07T12:40:00

Carsten Kossendey

leela

95000

1615000

0.014

-

-

2.158%

2014-04-10T20:52:00

ANONYMOUS

Manual testing

100000

0.008

-

-

0.772%

2014-05-09T20:32:00

Jocelyn Larouche

Manual testing

135993

0.011

-

-

0.924%

2014-09-19T20:39:00

Jocelyn Larouche

Manual testing

171986

0.014

-

-

1.051%

2015-06-01T09:50:00

mikr

MSI

2475400

86660000

0.556

-

-

7.333%

2018-07-02T12:39:36

Jocelyn Larouche

low 4M

1783261

178326100

0.897

-

-

7.939%

2018-10-19T12:14:54

Jocelyn Larouche

low 4M

1783261

196158710

0.973

-

-

8.047%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.022	-	-
2016-02-23T16:28:51	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.065	-	-
2010-04-21T13:12:00	Architects Cubed	m1_76l	2⁶⁰	2⁶¹		-	-	0.086	-	-
2016-02-23T16:28:51	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.172	-	-
2010-10-16T22:16:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.895	-	-
2016-02-23T16:28:51	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.550	-	-
2015-05-14T21:29:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.101	-	-
2015-05-14T21:29:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.095	-	-
2015-09-12T12:52:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.190	-	-
2018-01-22T18:13:16	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.381	-	-
2019-08-06T10:06:01	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	16.76	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.287 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:	17.287 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		248	17.08
50000	5000000	5493501031901936260553	3	0.207

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-23T23:29:00	paulie	iMac3.4	50000	5000000						3	0.207
2009-07-06T12:43:00	SubPrime	abd1	50000	5000000						3	0.207
2010-12-22T07:32:00	Lupo	yorick	50000	5000000						3	0.207
2012-02-19T15:02:00	S36049	Wolle5	50000	5000000						3	0.207
2013-06-17T18:16:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-02-18T05:26:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2015-02-13T07:28:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2015-09-24T16:09:16	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2016-01-28T05:35:46	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2016-03-29T05:32:40	Bruce	DESK3	50000	5000000						3	0.207
2016-05-12T07:02:37	Dennis Schreiber	z800	50000	5000000						3	0.207
2016-08-09T05:39:07	Bruce	DESK3	50000	5000000						3	0.207
2016-10-15T17:28:14	Bruce	DESK3	50000	5000000						3	0.207
2016-12-18T10:41:04	Bruce	DESK3	50000	5000000						3	0.207
2017-04-04T02:47:04	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2017-10-10T05:57:39	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2018-01-12T12:29:42	Bruce	DESK3	50000	5000000						3	0.207
2019-07-17T04:11:36	ANONYMOUS	TimeVampireTheFifth	50000	5000000						3	0.207
2019-11-19T04:26:28	George Woltman	colab	50000	5000000						3	0.207
2019-11-21T05:28:23	IanGlencross	glenx24	50000	5000000						3	0.207
2019-11-23T16:01:17	Sergey Nosov	TS140-02	50000	5000000						3	0.207
2019-11-25T14:04:53	daveward2005	Davy	50000	5000000						3	0.207
2019-11-29T03:54:58	Nesowa	entropy_generator_2	50000	5000000						3	0.207
2019-12-02T04:16:31	Nesowa	6700T	50000	5000000						3	0.207
2019-12-06T03:28:25	Alvin Bunk	i7-Core	50000	5000000						3	0.207
2019-12-11T00:13:23	mnd9	50871b	50000	5000000						3	0.207
2019-12-15T00:27:21	Keysarecool	HPLaptop	50000	5000000						3	0.207
2019-12-20T04:07:11	IanGlencross	glenx24	50000	5000000						3	0.207
2019-12-27T02:49:43	Alvin Bunk	BADCAT	50000	5000000						3	0.207
2020-01-02T20:57:24	Nesowa	entropy_generator_2	50000	5000000						3	0.207
2020-01-05T19:38:50	IanGlencross	glenx24	50000	5000000						3	0.207
2020-01-14T03:04:27	Alvin Bunk	BADCAT	50000	5000000						3	0.207
2020-01-22T06:07:35	Claude Portenier	Petit-Idiot	50000	5000000						3	0.207
2020-01-26T14:26:32	Sergey Nosov	TS140-02	50000	5000000						3	0.207
2020-02-04T04:56:39	Nesowa	6700T	50000	5000000						3	0.207
2020-02-12T13:30:45	Brett Walker	brain	50000	5000000						3	0.207
2020-02-19T09:13:26	mnd9	office2	50000	5000000						3	0.207
2020-02-26T09:29:32	Nesowa	6700T	50000	5000000						3	0.207
2020-03-04T04:51:27	ANONYMOUS	PC017	50000	5000000						3	0.207
2020-03-10T19:37:29	Keysarecool	HPLaptop	50000	5000000						3	0.207
2020-03-11T09:39:33	ANONYMOUS	Manual testing	50000	5000000						3	0.207
2020-03-29T15:57:18	Keysarecool	HPLaptop	50000	5000000						3	0.207
2020-04-10T21:11:20	mnd9	colab2	50000	5000000						3	0.207
2020-04-22T20:40:43	EricP	Cannonfodder	50000	5000000						3	0.207
2020-04-30T17:39:58	nordi	sweet16	50000	5000000						3	0.207
2020-05-11T18:11:17	nordi	sweet16	50000	5000000	5493501031901936260553	72.218	3	2	7169118833048946	3	0.207
2020-11-06T10:16:03	TJAOI	Manual testing	50000	5000000						113	7.782

date	userid	compid	res64	spent (GHz-days)
2015-07-18T18:31:00	MadPoo	Manual testing	90EC4DEC2774E069	0.097

date

userid

compid

res64

spent (GHz-days)

2015-07-18T18:31:00

MadPoo

Manual testing

90EC4DEC2774E069

0.097

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