M2255797 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	26.4230	67.6471%	1000000	20000000	0.1940	5.3765%	26.6170	69.3865%	1.7395%
PrimeNet	2⁵⁸	0.0170	62.0690%	10000	190000	0.0019	2.9176%	0.0189	63.1756%	1.1067%
GPU72	2⁶²	0.2723	64.5161%	12000	190000	0.0021	1.7056%	0.2744	65.1214%	0.6052%
Difference	+6	+26.1506	+3.1309%	+988000	+19810000	+0.1920	+3.6709%	+26.3426	+4.2652%	+4.2652%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2255797	524916403504711173706489	24	78.796	116348324672989452 2² × 3 × 131 × 5182157 × 14282263	2020-07-21	5182157	14282263	44,125	0.5413	1.0055

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%
2010-11-12T11:43:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.357%
2011-01-06T01:30:00	markr	tiny	100000	2075000		-		-	-	0.020	-	-	2.404%
2014-09-02T00:10:00	Jocelyn Larouche	Manual testing	128453	128453		-		-	-	0.012	-	-	0.933%
2016-03-02T12:01:16	Jocelyn Larouche	Manual testing	342144	6158592	12	-		-	-	0.063	-	-	3.758%
2019-06-28T03:46:10	BigBrother	Winston	1000000	20000000	12	-		-	-	0.194	-	-	5.377%

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	-	-
2009-01-11T04:10:00	Sturle Sunde	dietrich.ifi	2⁶⁰	2⁶¹		-	-	0.068	-	-
2012-05-04T16:48:00	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		-	-	0.870	-	-
2015-03-10T10:44:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.656	-	-
2015-10-29T11:36:23	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.313	-	-
2017-01-05T21:20:50	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.625	-	-
2019-05-13T13:38:17	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.25	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.473 GHz-days
Estimated T-Level:	4.350

Digits	B1	Curves	Complete	FacMiss
20	11000	87 / 100	0.870	41.712%
25	50000	87 / 280	0.311	73.252%

New Calculation Method

Total ECM effort:	7.473 GHz-days
Estimated T-Level:	4.350

Digits	B1	Complete	FacMiss
20	11000	2.806	6.042%
25	50000	0.254	77.597%
30	250000	0.016	98.450%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		84	7.215
50000	5000000	524916403504711173706489	3	0.258

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-29T00:34:00	Never Odd Or Even	Lap_Dir_2000	50000	5000000						3	0.258
2009-12-30T16:40:00	James Hintz	ryan	50000	5000000						3	0.258
2011-10-23T16:17:00	Bud	annan	50000	5000000						3	0.258
2013-08-09T01:59:00	Kripke	Kripke	50000	5000000						3	0.258
2015-03-31T16:14:00	Bruce	desk16	50000	5000000						3	0.258
2016-02-18T18:49:09	arnaud	CHAMOT09	50000	5000000						3	0.258
2016-06-01T10:48:00	Bruce	Desk6	50000	5000000						3	0.258
2016-07-20T00:22:56	Bruce	Desk6	50000	5000000						3	0.258
2016-12-06T08:51:13	Bruce	Desk6	50000	5000000						3	0.258
2017-07-02T16:00:09	Bruce	Desk6	50000	5000000						3	0.258
2017-12-16T18:06:06	Bruce	Desk6	50000	5000000						3	0.258
2018-05-25T21:45:29	Bruce	Desk6	50000	5000000						3	0.258
2019-05-23T17:12:48	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.258
2020-02-22T22:04:29	cappy95833	HomePC	50000	5000000						3	0.258
2020-02-29T13:23:34	mat10243x	B2	50000	5000000						3	0.258
2020-03-07T07:05:57	mnd9	25836b	50000	5000000						3	0.258
2020-03-14T21:00:23	mnd9	colab	50000	5000000						3	0.258
2020-03-22T12:28:33	daveward2005	Davy	50000	5000000						3	0.258
2020-04-03T15:10:40	daveward2005	Davy	50000	5000000						3	0.258
2020-04-17T16:51:12	Keysarecool	Boat_Anchor	50000	5000000						3	0.258
2020-04-26T10:33:35	daveward2005	Davy	50000	5000000						3	0.258
2020-05-05T06:56:27	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.258
2020-05-17T05:12:30	mnd9	libproj	50000	5000000						3	0.258
2020-06-05T15:12:32	Claude Portenier	Petit-Idiot	50000	5000000						3	0.258
2020-06-22T15:17:22	daveward2005	Davy	50000	5000000						3	0.258
2020-07-01T22:44:03	GAN	LMS-02	50000	5000000						3	0.258
2020-07-08T13:34:11	GAN	LMS-08	50000	5000000						3	0.258
2020-07-14T14:22:19	GAN	OSB-02	50000	5000000						3	0.258
2020-07-21T06:54:21	mnd9	libproj	50000	5000000	524916403504711173706489	78.796	3	2	4917118797070451	3	0.258

date	userid	compid	res64	spent (GHz-days)
1999-03-01T00:00:00	ANONYMOUS	v4_computers	DC9AABCC4D1F3725	0.148
2018-04-23T16:34:21	kkmrkkblmbrbk	old	DC9AABCC4D1F3725	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 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 342144, B2 = 6158592 (P-1 stage 2)

B1 = 342144 (P-1 stage 1)

B1 = 100000, B2 = 2075000 (P-1 stage 2)

B1 = 128453 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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