M2236207 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	26.6545	67.6471%	2000000	65000000	0.5179	7.0387%	27.1724	69.9243%	2.2772%
PrimeNet	2⁵⁸	0.0172	62.0690%	10000	180000	0.0018	2.8717%	0.0190	63.1582%	1.0893%
GPU72	2⁶²	0.2747	64.5161%	11000	190000	0.0020	1.6579%	0.2767	65.1044%	0.5883%
Difference	+6	+26.3797	+3.1309%	+1989000	+64810000	+0.5159	+5.3808%	+26.8957	+4.8199%	+4.8199%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2236207	2902471341922765345807	22	71.298	648971973954729 3² × 17 × 79 × 53691732767	2020-02-24	79	53691732767	347.53	278.89	520.89

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%
2010-11-07T12:40:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.675%
2011-01-14T01:54:00	Oscar Östlin		85000	1615000		-		-	-	0.016	-	-	2.185%
2014-06-01T23:28:00	Jocelyn Larouche	Manual testing	113702	113702		-		-	-	0.011	-	-	0.869%
2014-09-30T23:23:00	Jocelyn Larouche	Manual testing	142404	142404		-		-	-	0.014	-	-	0.987%
2015-12-01T19:51:22	Alexander Dubrovin	Manual testing	1000000	6000000	6	-		-	-	0.121	-	-	4.166%
2016-01-09T17:14:57	Alexander Dubrovin	Manual testing	2000000	65000000	12	-		-	-	0.518	-	-	7.039%

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	-	-
2009-01-11T01:08:00	Sturle Sunde	ghibu.ifi	2⁶⁰	2⁶¹		-	-	0.069	-	-
2012-04-27T05:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.137	-	-
2013-12-07T03:48:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.439	-	-
2015-03-10T10:44:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.878	-	-
2015-03-10T10:44:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.671	-	-
2015-10-25T20:35:12	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.342	-	-
2016-12-30T02:46:28	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.683	-	-
2019-04-08T13:40:38	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.37	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.775 GHz-days
Estimated T-Level:	2.200

Digits	B1	Curves	Complete	FacMiss
20	11000	44 / 100	0.440	64.261%
25	50000	44 / 280	0.157	85.434%

New Calculation Method

Total ECM effort:	3.775 GHz-days
Estimated T-Level:	2.200

Digits	B1	Complete	FacMiss
20	11000	1.419	24.187%
25	50000	0.128	87.961%
30	250000	0.008	99.213%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		42	3.603
50000	5000000	2902471341922765345807	2	0.172

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-25T00:37:00	Johan Koolwaaij	C0B5A3B75	50000	5000000						3	0.257
2009-12-25T04:18:00	wpolly	wpolly_02	50000	5000000						3	0.257
2011-10-06T08:01:00	S36049	Wolle5	50000	5000000						3	0.257
2013-12-25T05:17:00	Pool Party	St.P.p	50000	5000000						3	0.257
2015-03-23T16:16:00	Jason U	Server7	50000	5000000						3	0.257
2016-02-02T14:23:46	Cire Sivad	ServerEJAA	50000	5000000						3	0.257
2016-03-21T20:07:28	Bruce	Desk6	50000	5000000						3	0.257
2016-07-13T03:12:42	Bruce	Desk6	50000	5000000						3	0.257
2016-11-29T04:56:55	Bruce	Desk6	50000	5000000						3	0.257
2017-06-18T15:56:07	Bruce	Desk6	50000	5000000						3	0.257
2017-12-02T17:26:09	Bruce	Desk6	50000	5000000						3	0.257
2018-05-01T10:43:04	Bruce	Desk6	50000	5000000						3	0.257
2018-10-19T08:38:44	Bruce	Desk6	50000	5000000						3	0.257
2020-02-16T21:59:44	Alvin Bunk	BADCAT	50000	5000000						3	0.257
2020-02-24T05:30:17	mnd9	kitchen	50000	5000000	2902471341922765345807	71.298	2	2	8197289690746204	2	0.172

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	F970555B4A6EB266	0.147
2018-04-21T07:01:32	kkmrkkblmbrbk	old	F970555B4A6EB266	0.147

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 = 1000000, B2 = 6000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 85000, B2 = 1615000 (P-1 stage 2)

B1 = 142404 (P-1 stage 1)

B1 = 113702 (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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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