M2034481 Mersenne number exponent details

Residue

Status

L-L

47182E7AFF578E9C

double-checked

PRP

F9E6EB1505896E75

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	2⁶⁹	58.6817	69.5652%	4000000	200000000	1.3994	8.0927%	60.0811	72.0282%	2.4630%
PrimeNet	2⁵⁸	0.0189	63.7931%	9000	150000	0.0016	2.6155%	0.0205	64.7401%	0.9470%
GPU72	2⁶²	0.3020	66.1290%	9000	120000	0.0014	1.3282%	0.3034	66.5789%	0.4499%
Difference	+7	+58.3797	+3.4362%	+3991000	+199880000	+1.3980	+6.7645%	+59.7777	+5.4493%	+5.4493%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁹

58.6817

69.5652%

4000000

200000000

1.3994

8.0927%

60.0811

72.0282%

2.4630%

PrimeNet

2⁵⁸

0.0189

63.7931%

9000

150000

0.0016

2.6155%

0.0205

64.7401%

0.9470%

GPU72

2⁶²

0.3020

66.1290%

9000

120000

0.0014

1.3282%

0.3034

66.5789%

0.4499%

Difference

+58.3797

+3.4362%

+3991000

+199880000

+1.3980

+6.7645%

+59.7777

+5.4493%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2034481	10796459437886874701252377	26	83.159	2653369443579683148 2² × 3 × 17 × 47 × 45503 × 6081765457	2021-09-16	45503	6081765457	1,735,661	31.594	59.002

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2034481

10796459437886874701252377

83.159

2653369443579683148
2² × 3 × 17 × 47 × 45503 × 6081765457

2021-09-16

45503

6081765457

1,735,661

31.594

59.002

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2003-02-24T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.178%
2009-01-29T23:09:00	markr	Manual testing	100000	3000000		-		-	-	0.025	-	-	2.287%
2014-07-04T02:22:00	Jocelyn Larouche	Manual testing	131548	131548		-		-	-	0.013	-	-	0.808%
2014-10-17T00:38:00	Jocelyn Larouche	Manual testing	163096	163096		-		-	-	0.016	-	-	0.913%
2015-10-05T10:35:08	Bruno Victal	4790K-windows	500000	15000000	12	-		-	-	0.123	-	-	4.224%
2019-05-16T15:45:19	mikr	MSI	4000000	200000000	12	-		-	-	1.399	-	-	8.093%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2003-02-24T00:00:00

ANONYMOUS

v4_computers

2048

204800

0.001

-

-

0.178%

2009-01-29T23:09:00

markr

Manual testing

100000

3000000

0.025

-

-

2.287%

2014-07-04T02:22:00

Jocelyn Larouche

Manual testing

131548

0.013

-

-

0.808%

2014-10-17T00:38:00

Jocelyn Larouche

Manual testing

163096

0.016

-

-

0.913%

2015-10-05T10:35:08

Bruno Victal

4790K-windows

500000

15000000

0.123

-

-

4.224%

2019-05-16T15:45:19

mikr

MSI

4000000

200000000

1.399

-

-

8.093%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-10T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2016-02-23T16:29:04	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.057	-	-
2009-01-02T22:06:00	Sturle Sunde	gimba.ifi	2⁶⁰	2⁶¹		-	-	0.075	-	-
2012-02-10T16:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.151	-	-
2013-08-29T08:26:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.483	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.965	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.837	-	-
2015-11-01T21:50:57	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.673	-	-
2016-07-29T19:18:38	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.346	-	-
2019-03-20T02:02:08	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	14.69	-	-
2021-07-29T11:14:51	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	29.38	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.443 GHz-days
Estimated T-Level:	23.643

Digits	B1	Curves	Complete	FacMiss
20	11000	204 / 100	2.040	12.870%
25	50000	204 / 280	0.729	48.197%

New Calculation Method

Total ECM effort:	17.443 GHz-days
Estimated T-Level:	23.643

Digits	B1	Complete	FacMiss
20	11000	6.604	0.136%
25	50000	0.598	54.997%
30	250000	0.037	96.377%
35	1000000	0.002	99.831%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		196	16.61
50000	5000000	10796459437886874701252377	7	0.593
76620	23259610		1	0.237

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-05T04:16:00	SubPrime	dijkstra	50000	5000000						3	0.254
2009-09-16T01:29:00	lindee	tanagra	50000	5000000						3	0.254
2011-02-24T19:28:00	Lupo	yorick	50000	5000000						3	0.254
2013-02-26T03:12:00	Donna Noble	opt4820	50000	5000000						3	0.254
2014-03-20T10:28:00	Bruce	snowflake	50000	5000000						3	0.254
2015-07-19T03:35:00	dragon325	Falken-i7-920	50000	5000000						3	0.254
2016-01-07T16:02:17	mikr	MSI	50000	5000000						12	1.017
2017-05-17T01:13:41	Bruce	Desk6	50000	5000000						3	0.254
2017-11-18T10:34:42	Bruce	Desk6	50000	5000000						3	0.254
2018-03-25T18:37:48	Bruce	Desk6	50000	5000000						3	0.254
2018-09-03T22:05:50	Bruce	Desk6	50000	5000000						3	0.254
2019-12-21T03:09:26	daveward2005	Davy	50000	5000000						3	0.254
2019-12-28T13:28:38	mnd9	colab	50000	5000000						3	0.254
2020-01-01T13:46:27	Brett Walker	brain	50000	5000000						3	0.254
2020-01-06T21:18:35	Keysarecool	HPLaptop	50000	5000000						3	0.254
2020-01-14T20:14:40	EricP	Cannonfodder	50000	5000000						3	0.254
2020-01-21T14:06:09	David_McCann	i5	50000	5000000						3	0.254
2020-01-27T09:42:39	EricP	Cannonfodder	50000	5000000						3	0.254
2020-02-06T01:59:13	cappy95833	HomePC	50000	5000000						3	0.254
2020-02-13T12:38:12	mnd9	libproj	50000	5000000						3	0.254
2020-02-21T04:08:02	Alvin Bunk	BADCAT	50000	5000000						3	0.254
2020-02-27T04:32:42	Nesowa	6700T	50000	5000000						3	0.254
2020-03-05T13:47:40	Brett Walker	brain	50000	5000000						3	0.254
2020-03-11T16:48:08	EricP	Cannonfodder	50000	5000000						3	0.254
2020-03-19T16:42:17	mnd9	27016b	50000	5000000						3	0.254
2020-03-31T20:54:44	mnd9	office	50000	5000000						3	0.254
2020-04-13T07:17:14	Keysarecool	HPLaptop	50000	5000000						3	0.254
2020-04-23T22:06:54	EricP	Cannonfodder	50000	5000000						3	0.254
2020-05-01T19:33:38	CrypticClue	cruncher	50000	5000000						3	0.254
2020-05-13T10:14:30	mnd9	libproj	50000	5000000						3	0.254
2020-05-29T09:25:52	mnd9	libproj	50000	5000000						3	0.254
2020-06-18T02:37:45	GAN	KL-SCH05	50000	5000000						3	0.254
2020-06-29T19:00:54	nordi	sweet16	50000	5000000						3	0.254
2020-07-06T13:49:20	GAN	LMS-02	50000	5000000						3	0.254
2020-07-12T23:06:46	GAN	LMS-11	50000	5000000						3	0.254
2020-07-19T01:44:32	daveward2005	Dave2	50000	5000000						3	0.254
2020-07-25T03:50:41	GAN	LMS-06	50000	5000000						3	0.254
2020-08-01T16:42:34	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.254
2020-08-09T06:59:07	J.R. Allen	lapasus	50000	5000000						3	0.254
2020-08-19T21:48:32	M. R. Mayer	nimbus	50000	5000000						7	0.593
2020-09-21T11:46:55	mat10243x	K2	50000	5000000						7	0.593
2020-10-20T18:06:55	tottenhoff	Garage-Band-003	50000	5000000						7	0.593
2020-11-07T13:12:13	Bruno Victal	Manual testing	76620	23259610						1	0.237
2020-12-13T22:18:26	rextherunt	ice	50000	5000000						7	0.593
2021-01-14T03:50:01	Zenzoma	AMD3970X	50000	5000000						7	0.593
2021-02-13T05:00:53	Gerry Snyder	Gerry-Workstation	50000	5000000						7	0.593
2021-03-13T23:35:15	mnd9	75204	50000	5000000						7	0.593
2021-04-22T22:05:22	daveward2005	Dave2	50000	5000000						7	0.593
2021-06-11T17:45:17	daveward2005	Dave2	50000	5000000						7	0.593
2021-07-24T02:14:44	Jew	Jew-DO-Droplet	50000	5000000						7	0.593
2021-09-16T16:19:36	mnd9	27016b	50000	5000000	10796459437886874701252377	83.159	7	2	1826114992608310	7	0.593

date	userid	compid	res64	spent (GHz-days)
1999-02-07T00:00:00	ANONYMOUS	v4_computers	47182E7AFF578E9C	0.134
2016-07-15T17:22:16	Mark Rose	leonardo	47182E7AFF578E9C	0.134

date

userid

compid

res64

spent (GHz-days)

1999-02-07T00:00:00

ANONYMOUS

v4_computers

47182E7AFF578E9C

0.134

2016-07-15T17:22:16

Mark Rose

leonardo

47182E7AFF578E9C

0.134

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