M2451011 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	2⁶⁹	48.7092	68.1159%	1172000	48000000	0.3647	5.8886%	49.0739	69.9935%	1.8775%
PrimeNet	2⁵⁹	0.0313	62.7119%	10000	180000	0.0019	2.5285%	0.0332	63.6547%	0.9428%
GPU72	2⁶³	0.6512	65.0794%	10000	160000	0.0018	1.3335%	0.6529	65.5450%	0.4657%
Difference	+6	+48.0580	+3.0366%	+1162000	+47840000	+0.3629	+4.5551%	+48.4210	+4.4484%	+4.4484%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2451011	350830009076427803936113	24	78.215	71568428105061096 2³ × 3 × 11 × 19 × 14268027931631	2021-12-09	19	14268027931631	30,685	76,147	142,221

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2003-10-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.188%
2003-10-31T00:00:00	Team Prime Rib	v4_computers	15000	232500		-		-	-	0.003	-	-	0.672%
2010-12-15T23:00:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.220%
2011-01-18T13:55:00	Oscar Östlin		95000	1947500		-		-	-	0.019	-	-	2.103%
2014-02-01T03:43:00	mikr	MSI	1172000	48000000		-		-	-	0.365	-	-	5.889%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.031	-	-
2016-02-23T16:29:14	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.031	-	-
2009-01-14T21:05:00	Sturle Sunde	wright.ifi	2⁶⁰	2⁶¹		-	-	0.063	-	-
2012-06-07T07:42:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.125	-	-
2013-12-04T21:13:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.401	-	-
2015-02-27T20:41:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.801	-	-
2015-02-27T20:41:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.524	-	-
2015-10-25T20:35:04	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.049	-	-
2017-07-14T10:08:12	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.098	-	-
2019-07-17T09:51:52	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.20	-	-
2021-06-10T09:21:51	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	24.39	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	13.571 GHz-days
Estimated T-Level:	22.661

Digits	B1	Curves	Complete	FacMiss
20	11000	150 / 100	1.500	22.145%
25	50000	149 / 280	0.532	58.679%

New Calculation Method

Total ECM effort:	13.571 GHz-days
Estimated T-Level:	22.661

Digits	B1	Complete	FacMiss
20	11000	4.869	0.768%
25	50000	0.441	64.363%
30	250000	0.027	97.322%
35	1000000	0.001	99.876%

ECM Summary

B1	B2	factor	curves	GHz-days
47000	4700000		1	0.084
50000	5000000		128	11.43
50000	5000000	350830009076427803936113	7	0.625
50000	6750000		14	1.434

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-11T19:07:00	Sturle Sunde	PRECZC51100MQ	50000	5000000						3	0.268
2010-03-12T20:03:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.268
2012-04-26T15:07:00	Lukasz Wrobel	i-1	50000	5000000						3	0.268
2014-01-03T22:32:00	Andy Incline	Office-PC	50000	5000000						3	0.268
2015-07-09T08:25:00	guru	w6	50000	5000000						3	0.268
2016-04-24T16:53:02	lettp	Home	50000	5000000						3	0.268
2016-06-16T16:59:47	lettp	Home	50000	5000000						3	0.268
2016-10-31T02:46:02	Bruce	Desk6	50000	5000000						3	0.268
2017-05-05T11:27:36	Bruce	Desk6	50000	5000000						3	0.268
2017-12-04T15:39:30	Sebastian Hornbostel	V2	50000	5000000						3	0.268
2018-05-22T21:17:54	Bruce	Desk6	50000	5000000						3	0.268
2019-06-28T10:32:59	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.268
2020-04-28T10:59:02	mnd9	fb	50000	5000000						3	0.268
2020-05-08T20:17:49	Keysarecool	Boat_Anchor	50000	5000000						3	0.268
2020-05-23T09:18:24	mnd9	75203b	50000	5000000						3	0.268
2020-06-10T09:01:18	daveward2005	Davy	50000	5000000						3	0.268
2020-06-26T05:58:54	daveward2005	Davy	50000	5000000						3	0.268
2020-07-04T20:04:50	LaurV	3tits	50000	5000000						3	0.268
2020-07-10T12:06:21	GAN	LMS-03	50000	5000000						3	0.268
2020-07-16T10:26:20	daveward2005	Dave2	50000	5000000						3	0.268
2020-07-22T13:03:55	GAN	LMS-03	50000	5000000						3	0.268
2020-07-29T21:33:49	GAN	AC-KL	50000	5000000						3	0.268
2020-08-05T18:38:00	IanGlencross	glenx24	50000	5000000						3	0.268
2020-08-14T09:10:53	rextherunt	ice	50000	5000000						3	0.268
2020-09-05T02:46:45	GAN	OSB-01	50000	5000000						7	0.625
2020-10-07T19:03:00	daveward2005	Dave2	50000	5000000						7	0.625
2020-11-04T18:59:21	GAN	KA-HP	50000	5000000						7	0.625
2020-12-09T12:45:34	Peredron	Peredron2	47000	4700000						1	0.084
2020-12-17T09:33:18	lycorn	colab_ES	50000	5000000						7	0.625
2021-01-19T06:21:38	Chang Chia-Tche	ex-ctcpc	50000	5000000						7	0.625
2021-02-17T07:56:11	mnd9	27016b	50000	5000000						7	0.625
2021-03-18T06:59:59	Gerry Snyder	Gerry-Workstation	50000	5000000						7	0.625
2021-06-16T21:28:57	LaurV	butu	50000	6750000						7	0.717
2021-07-30T19:59:44	kutens	ryzen2	50000	6750000						7	0.717
2021-08-10T13:00:51	Gerry Snyder	Gerry-Workstation	50000	5000000						7	0.625
2021-12-09T02:48:23	daveward2005	Dave2	50000	5000000	350830009076427803936113	78.215	7	2	574638978070213	7	0.625

date	userid	compid	res64	spent (GHz-days)
1999-04-13T00:00:00	ANONYMOUS	v4_computers	D1D76D201634B933	0.166
2018-05-26T06:15:19	kkmrkkblmbrbk	old	D1D76D201634B933	0.166

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 = 1172000, B2 = 48000000 (P-1 stage 2)

B1 = 1172000 (P-1 stage 1)

B1 = 95000, B2 = 1947500 (P-1 stage 2)

B1 = 95000 (P-1 stage 1)

B1 = 15000, B2 = 232500 (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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

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