M2694641 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	22.1198	67.6471%	8000000	250000000	2.3725	9.6908%	24.4923	70.7823%	3.1352%
PrimeNet	2⁵⁹	0.0285	62.7119%	12000	220000	0.0026	2.8420%	0.0311	63.7716%	1.0597%
GPU72	2⁶³	0.5923	65.0794%	14000	220000	0.0028	1.6606%	0.5951	65.6593%	0.5799%
Difference	+5	+21.5275	+2.5677%	+7986000	+249780000	+2.3697	+8.0301%	+23.8972	+5.1230%	+5.1230%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2694641	2239494221587833302000687	25	80.889	415545933871679623 47 × 101 × 87538642062709	2020-11-24	101	87538642062709	125,942	534,130	997,607

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.240%
2003-11-28T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.787%
2010-12-22T11:37:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.268%
2010-12-26T02:29:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.371%
2011-01-15T16:05:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.537%
2011-03-05T04:31:00	James Heinrich	i7-920	300000	8000000		-		-	-	0.081	-	-	3.988%
2018-07-17T21:33:40	Jocelyn Larouche	low 4M	600000	6000000	6	-		-	-	0.100	-	-	4.078%
2018-08-12T11:43:41	mikr	S067	8000000	250000000	12	-		-	-	2.373	-	-	9.691%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:19	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.057	-	-
2009-01-30T19:26:00	Sturle Sunde	kraus.ifi	2⁶⁰	2⁶¹		-	-	0.057	-	-
2012-05-02T06:59:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.114	-	-
2013-01-14T12:26:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.364	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.729	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.387	-	-
2016-01-27T13:46:24	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.773	-	-
2017-09-15T16:43:52	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.546	-	-
2019-03-18T11:45:37	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.09	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.041 GHz-days
Estimated T-Level:	3.400

Digits	B1	Curves	Complete	FacMiss
20	11000	68 / 100	0.680	50.489%
25	50000	68 / 280	0.243	78.404%

New Calculation Method

Total ECM effort:	7.041 GHz-days
Estimated T-Level:	3.400

Digits	B1	Complete	FacMiss
20	11000	2.194	11.152%
25	50000	0.198	82.016%
30	250000	0.012	98.787%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		63	6.523
50000	5000000	2239494221587833302000687	5	0.518

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-15T06:49:00	Tom Bammann	Work2	50000	5000000						3	0.311
2010-08-02T23:21:00	Mark Grant	EVGA-X58-SLI	50000	5000000						3	0.311
2013-01-05T19:11:00	Sara	Sara	50000	5000000						3	0.311
2015-01-11T17:12:00	George Daubert	Gateway	50000	5000000						3	0.311
2016-04-13T20:39:22	AnthonyRais		50000	5000000						3	0.311
2016-04-28T00:42:15	lettp	Home	50000	5000000						3	0.311
2016-12-26T03:14:22	Ensigma	vps_sing	50000	5000000						3	0.311
2017-07-12T00:42:28	AnthonyRais	Win10Test	50000	5000000						3	0.311
2017-11-22T05:33:45	Sebastian Hornbostel	V2	50000	5000000						3	0.311
2018-06-24T12:36:36	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.311
2019-09-26T05:49:14	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.311
2020-08-02T00:12:42	Sergey Nosov	TS140-02	50000	5000000						3	0.311
2020-08-09T06:46:14	GAN	LMS-02	50000	5000000						3	0.311
2020-08-21T12:59:32	mnd9	libproj	50000	5000000						7	0.725
2020-09-09T21:19:25	mnd9	75204b	50000	5000000						3	0.311
2020-09-28T22:28:41	LaurV	bc1	50000	5000000						7	0.725
2020-10-22T22:55:18	mnd9	75203b	50000	5000000						7	0.725
2020-11-24T13:32:36	daveward2005	Dave2	50000	5000000	2239494221587833302000687	80.889	5	2	3968785025155812	5	0.518

date	userid	compid	res64	spent (GHz-days)
1998-06-29T00:00:00	ANONYMOUS	v4_computers	A96ADE111E7B2CA6	0.208
1999-04-23T00:00:00	MadPoo	v4_computers	A96ADE111E7B2CA6	0.208
2018-07-29T23:16:30	kkmrkkblmbrbk	old	A96ADE111E7B2CA6	0.208

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 8000000, B2 = 250000000 (P-1 stage 2)

B1 = 8000000 (P-1 stage 1)

B1 = 600000, B2 = 6000000 (P-1 stage 2)

B1 = 300000, B2 = 8000000 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 217500 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

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