M2226251 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	26.7737	67.6471%	2000000	65000000	0.5179	7.0355%	27.2916	69.9232%	2.2762%
PrimeNet	2⁵⁸	0.0172	62.0690%	10000	180000	0.0018	2.8693%	0.0191	63.1573%	1.0884%
GPU72	2⁶²	0.2760	64.5161%	11000	180000	0.0019	1.6308%	0.2779	65.0948%	0.5787%
Difference	+6	+26.4977	+3.1309%	+1989000	+64820000	+0.5160	+5.4047%	+27.0137	+4.8284%	+4.8284%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2226251	414901951563666406151287	24	78.457	93184001166909393 3² × 13 × 103 × 7732470431243	2020-07-02	103	7732470431243	48,407	40,164	75,016

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.227%
2010-10-22T06:48:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.675%
2011-01-13T02:16:00	Oscar Östlin		85000	1593750		-		-	-	0.016	-	-	2.176%
2014-05-26T23:57:00	Jocelyn Larouche	Manual testing	113831	113831		-		-	-	0.011	-	-	0.869%
2014-09-29T22:04:00	Jocelyn Larouche	Manual testing	142662	142662		-		-	-	0.014	-	-	0.987%
2015-05-04T02:45:00	Squeeky_Squirrel	P4_2600	160000	4600000		-		-	-	0.038	-	-	3.137%
2015-11-22T12:09:30	Alexander Dubrovin	Manual testing	1000000	5000000	6	-		-	-	0.116	-	-	3.984%
2015-11-22T12:09:30	Alexander Dubrovin	Manual testing	1600000	7000000	6	-		-	-	0.181	-	-	4.455%
2015-12-25T17:48:45	Alexander Dubrovin	Manual testing	2000000	65000000	12	-		-	-	0.518	-	-	7.035%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-02-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.017	-	-
2016-02-23T16:29:09	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.052	-	-
2009-01-10T23:50:00	Sturle Sunde	hummel.ifi	2⁶⁰	2⁶¹		-	-	0.069	-	-
2012-04-19T19:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.138	-	-
2013-12-03T17:40:00	LaurV	Manual testing	2⁶²	2⁶³		-	-	0.441	-	-
2015-03-06T11:16:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.882	-	-
2015-03-06T11:16:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.678	-	-
2015-10-25T20:35:09	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.357	-	-
2016-12-24T00:00:59	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.713	-	-
2019-04-15T13:43:07	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.43	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.031 GHz-days
Estimated T-Level:	4.100

Digits	B1	Curves	Complete	FacMiss
20	11000	82 / 100	0.820	43.862%
25	50000	82 / 280	0.293	74.574%

New Calculation Method

Total ECM effort:	7.031 GHz-days
Estimated T-Level:	4.100

Digits	B1	Complete	FacMiss
20	11000	2.645	7.099%
25	50000	0.239	78.736%
30	250000	0.015	98.539%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		79	6.774
50000	5000000	414901951563666406151287	3	0.257

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-27T06:15:00	mdrg	MDRG02	50000	5000000						3	0.257
2010-04-24T17:43:00	James Hintz	nana	50000	5000000						3	0.257
2011-09-29T21:17:00	Andriy Makukha	asus-laptop	50000	5000000						3	0.257
2013-06-15T15:37:00	jim f in mn	asus	50000	5000000						3	0.257
2015-03-20T10:26:00	Bruce	desk16	50000	5000000						3	0.257
2016-01-26T14:34:58	Jason U	Server7	50000	5000000						3	0.257
2016-03-18T18:47:01	Bruce	Desk6	50000	5000000						3	0.257
2016-07-16T20:25:54	lettp	Home	50000	5000000						3	0.257
2016-11-24T18:47:14	Bruce	Desk6	50000	5000000						3	0.257
2017-01-24T23:30:16	Alexander Dubrovin	Manual testing	50000	5000000						1	0.086
2017-08-15T02:44:18	Bruce	Desk6	50000	5000000						3	0.257
2018-01-10T07:26:19	Bruce	Desk6	50000	5000000						3	0.257
2018-07-01T13:18:28	Bruce	Desk6	50000	5000000						3	0.257
2019-08-20T09:27:47	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.257
2020-02-16T04:33:46	mnd9	libproj	50000	5000000						3	0.257
2020-02-23T03:15:01	CrypticClue	cruncher	50000	5000000						3	0.257
2020-02-29T19:27:33	daveward2005	Davy	50000	5000000						3	0.257
2020-03-07T02:29:31	mnd9	office2	50000	5000000						3	0.257
2020-03-14T19:52:53	kracker	O0	50000	5000000						3	0.257
2020-03-22T17:02:01	kracker	O0	50000	5000000						3	0.257
2020-04-04T08:21:20	daveward2005	MW	50000	5000000						3	0.257
2020-04-18T03:17:24	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.257
2020-04-26T16:06:09	mnd9	office2	50000	5000000						3	0.257
2020-05-07T02:49:44	Massimo Cappelli (ik5pwa)	maxlinux_3	50000	5000000						3	0.257
2020-05-17T01:13:55	quantizedSpacetime	zach	50000	5000000						3	0.257
2020-06-04T16:16:23	Sergey Nosov	TS140-02	50000	5000000						3	0.257
2020-06-22T16:02:09	MarkS	desktop-i7	50000	5000000						3	0.257
2020-07-02T04:53:28	GAN	OSB-01	50000	5000000	414901951563666406151287	78.457	3	2	3479966784248000	3	0.257

date	userid	compid	res64	spent (GHz-days)
1999-02-21T00:00:00	ANONYMOUS	v4_computers	9D73BD56C0ABA470	0.146
2018-04-19T22:38:31	kkmrkkblmbrbk	old	9D73BD56C0ABA470	0.146

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 = 2000000, B2 = 65000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 1600000, B2 = 7000000 (P-1 stage 2)

B1 = 1600000 (P-1 stage 1)

B1 = 1000000, B2 = 5000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 160000, B2 = 4600000 (P-1 stage 2)

B1 = 85000, B2 = 1593750 (P-1 stage 2)

B1 = 160000 (P-1 stage 1)

B1 = 142662 (P-1 stage 1)

B1 = 113831 (P-1 stage 1)

B1 = 85000 (P-1 stage 1)

B1 = 75011 (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

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