M2953571 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	20.1806	67.6471%	1072727	22000000	0.2731	5.6813%	20.4537	69.4851%	1.8381%
PrimeNet	2⁶⁰	0.0520	63.3333%	12000	220000	0.0029	2.5079%	0.0549	64.2529%	0.9196%
GPU72	2⁶⁴	1.2051	65.6250%	12000	200000	0.0027	1.3470%	1.2078	66.0880%	0.4630%
Difference	+4	+18.9755	+2.0221%	+1060727	+21800000	+0.2704	+4.3343%	+19.2459	+3.3971%	+3.3971%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2953571	30797505854422224751199	23	74.705	5213605133315269 8513 × 612428654213	2020-09-14	8513	612428654213	1,359.5	4,117.8	7,691.0

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-13T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.247%
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.146%
2010-11-02T15:37:00	markr	tiny	95000	1995000		-		-	-	0.024	-	-	2.457%
2014-11-12T02:17:00	Jocelyn Larouche	Manual testing	116731	116731		-		-	-	0.014	-	-	0.928%
2015-01-26T18:12:00	Jocelyn Larouche	Manual testing	141244	141244		-		-	-	0.017	-	-	1.032%
2015-01-31T14:55:00	Jocelyn Larouche	Manual testing	170904	170904		-		-	-	0.021	-	-	1.144%
2015-02-01T13:32:00	Jocelyn Larouche	Manual testing	187994	187994		-		-	-	0.023	-	-	1.202%
2015-02-04T11:55:00	Jocelyn Larouche	Manual testing	413586	413586		-		-	-	0.051	-	-	1.755%
2015-02-25T03:47:00	Jocelyn Larouche	Manual testing	454944	454944		-		-	-	0.056	-	-	1.830%
2015-03-02T13:10:00	Jocelyn Larouche	Manual testing	500438	500438		-		-	-	0.062	-	-	1.907%
2015-03-12T10:39:00	Jocelyn Larouche	Manual testing	550481	550481		-		-	-	0.068	-	-	1.986%
2015-03-14T11:30:00	Jocelyn Larouche	Manual testing	605529	605529		-		-	-	0.075	-	-	2.067%
2015-03-29T20:50:00	Jocelyn Larouche	Manual testing	732689	732689		-		-	-	0.090	-	-	2.234%
2015-04-08T16:59:00	Jocelyn Larouche	Manual testing	805957	805957		-		-	-	0.099	-	-	2.320%
2015-05-01T17:21:00	Jocelyn Larouche	Manual testing	975207	975207		-		-	-	0.120	-	-	2.498%
2015-05-08T13:54:00	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.251	-	-	5.544%
2016-09-05T18:36:02	Jocelyn Larouche	low4M	1072727	22000000	12	-		-	-	0.273	-	-	5.681%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-07-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.052	-	-
2009-02-13T19:35:00	Sturle Sunde	akerman.ifi	2⁶⁰	2⁶¹		-	-	0.052	-	-
2011-12-18T20:34:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.104	-	-
2013-01-07T13:49:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.332	-	-
2015-04-27T09:54:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.665	-	-
2015-04-27T09:54:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.265	-	-
2016-02-26T10:03:32	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.530	-	-
2017-11-28T10:01:37	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.060	-	-
2018-12-24T00:53:33	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.12	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.317 GHz-days
Estimated T-Level:	1.000

Digits	B1	Curves	Complete	FacMiss
20	11000	20 / 100	0.200	81.791%
25	50000	20 / 280	0.071	93.094%

New Calculation Method

Total ECM effort:	2.317 GHz-days
Estimated T-Level:	1.000

Digits	B1	Complete	FacMiss
20	11000	0.645	52.458%
25	50000	0.058	94.336%
30	250000	0.004	99.642%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		18	2.085
50000	5000000	30797505854422224751199	2	0.232

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-03T05:47:00	alan145	Bear4	50000	5000000						3	0.347
2011-04-22T07:53:00	Pool Party	desk_1	50000	5000000						3	0.347
2013-07-07T20:48:00	Bruce	fx6840-21	50000	5000000						3	0.347
2016-01-02T20:26:58	Bruce	Desk7	50000	5000000						3	0.347
2017-06-08T15:45:39	Bruce	Desk10	50000	5000000						3	0.347
2019-10-15T17:32:09	Claude Portenier	Petit-Idiot	50000	5000000						3	0.347
2020-09-14T12:48:09	GAN	OSB-01	50000	5000000	30797505854422224751199	74.705	2	2	4596334274559612	2	0.232

date	userid	compid	res64	spent (GHz-days)
2015-11-14T06:50:09	MadPoo	Manual testing	E10F09944109C447	0.251

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 = 1072727, B2 = 22000000 (P-1 stage 2)

B1 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 1072727 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 975207 (P-1 stage 1)

B1 = 805957 (P-1 stage 1)

B1 = 732689 (P-1 stage 1)

B1 = 605529 (P-1 stage 1)

B1 = 550481 (P-1 stage 1)

B1 = 500438 (P-1 stage 1)

B1 = 454944 (P-1 stage 1)

B1 = 413586 (P-1 stage 1)

B1 = 95000, B2 = 1995000 (P-1 stage 2)

B1 = 187994 (P-1 stage 1)

B1 = 170904 (P-1 stage 1)

B1 = 141244 (P-1 stage 1)

B1 = 116731 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

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

B1 = 10000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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