M2254517 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	26.4380	67.6471%	589050	5890500	0.0837	3.9640%	26.5217	68.9295%	1.2825%
PrimeNet	2⁵⁸	0.0170	62.0690%	10000	190000	0.0019	2.9173%	0.0189	63.1755%	1.1066%
GPU72	2⁶²	0.2725	64.5161%	12000	190000	0.0021	1.7054%	0.2746	65.1213%	0.6052%
Difference	+6	+26.1655	+3.1309%	+577050	+5700500	+0.0816	+2.2586%	+26.2471	+3.8083%	+3.8083%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2254517	508129771933443512407	21	68.784	112691492664159 3 × 23 × 67 × 24376269233	2020-03-06	67	24376269233	33.205	126.62	236.48

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-04-03T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.228%
2010-11-06T12:26:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.200%
2010-11-14T20:17:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.257%
2010-11-24T02:13:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.676%
2011-01-16T13:31:00	Oscar Östlin		85000	1636250		-		-	-	0.016	-	-	2.195%
2014-06-03T02:15:00	Jocelyn Larouche	Manual testing	113469	113469		-		-	-	0.011	-	-	0.869%
2014-10-03T21:04:00	Jocelyn Larouche	Manual testing	141938	141938		-		-	-	0.014	-	-	0.987%
2016-01-20T23:38:51	Jocelyn Larouche	Manual testing	589050	5890500	6	-		-	-	0.084	-	-	3.964%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:10	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.068	-	-
2009-01-11T11:41:00	Sturle Sunde	golan.ifi	2⁶⁰	2⁶¹		-	-	0.068	-	-
2012-05-04T15:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.136	-	-
2013-01-23T08:24:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.435	-	-
2015-03-10T10:44:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.871	-	-
2015-03-10T10:44:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.657	-	-
2015-10-28T09:42:38	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.315	-	-
2017-01-05T21:20:50	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.629	-	-
2019-05-20T13:24:27	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.26	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.037 GHz-days
Estimated T-Level:	2.350

Digits	B1	Curves	Complete	FacMiss
20	11000	47 / 100	0.470	62.353%
25	50000	47 / 280	0.168	84.522%

New Calculation Method

Total ECM effort:	4.037 GHz-days
Estimated T-Level:	2.350

Digits	B1	Complete	FacMiss
20	11000	1.516	21.956%
25	50000	0.137	87.195%
30	250000	0.008	99.160%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		45	3.865
50000	5000000	508129771933443512407	2	0.172

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-26T15:47:00	Smurgs	Praca	50000	5000000						3	0.258
2009-12-30T23:04:00	SubPrime	abd0	50000	5000000						3	0.258
2011-10-22T17:09:00	Bud	annan	50000	5000000						3	0.258
2013-08-08T16:05:00	hiems	Laptop	50000	5000000						3	0.258
2015-04-12T17:11:00	dragon325	Falken-i7-920	50000	5000000						3	0.258
2016-02-03T09:12:42	Jason U	Server7	50000	5000000						3	0.258
2016-04-03T11:27:11	S36049	Wolle5	50000	5000000						3	0.258
2016-07-19T10:59:27	Bruce	Desk6	50000	5000000						3	0.258
2016-12-05T20:30:25	Bruce	Desk6	50000	5000000						3	0.258
2017-07-01T18:33:39	Bruce	Desk6	50000	5000000						3	0.258
2017-12-15T18:59:37	Bruce	Desk6	50000	5000000						3	0.258
2018-05-24T01:07:59	Bruce	Desk6	50000	5000000						3	0.258
2019-05-18T15:36:18	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.258
2020-02-22T15:46:06	Keysarecool	Boat_Anchor	50000	5000000						3	0.258
2020-02-28T22:57:08	IanGlencross	glenx24	50000	5000000						3	0.258
2020-03-06T12:17:18	Keysarecool	HPLaptop	50000	5000000	508129771933443512407	68.784	2	2	2953034744439243	2	0.172

date	userid	compid	res64	spent (GHz-days)
1999-03-01T00:00:00	ANONYMOUS	v4_computers	33C3953519271EE0	0.148
2018-04-23T12:55:06	kkmrkkblmbrbk	old	33C3953519271EE0	0.148

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 = 589050, B2 = 5890500 (P-1 stage 2)

B1 = 589050 (P-1 stage 1)

B1 = 85000, B2 = 1636250 (P-1 stage 2)

B1 = 141938 (P-1 stage 1)

B1 = 113469 (P-1 stage 1)

B1 = 85000 (P-1 stage 1)

B1 = 75011 (P-1 stage 1)

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

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