M2145389 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	27.7828	67.6471%	2500000	125000000	0.8746	7.9152%	28.6574	70.2079%	2.5608%
PrimeNet	2⁵⁸	0.0179	62.0690%	9000	170000	0.0017	2.7326%	0.0196	63.1055%	1.0365%
GPU72	2⁶²	0.2864	64.5161%	10000	150000	0.0017	1.4883%	0.2880	65.0442%	0.5281%
Difference	+6	+27.4964	+3.1309%	+2490000	+124850000	+0.8730	+6.4269%	+28.3694	+5.1636%	+5.1636%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2145389	3723368062513511308520257	25	81.623	867760593186949152 2⁵ × 3 × 373 × 21821 × 1110568139	2020-02-08	21821	1110568139	311,874	5.7705	10.774

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.225%
2010-11-03T01:56:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.254%
2010-12-30T22:20:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.353%
2011-01-13T23:58:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.512%
2011-01-21T14:55:00	James Heinrich	i7-920	130000	2632500		-		-	-	0.025	-	-	2.654%
2014-11-01T00:51:00	Jocelyn Larouche	Manual testing	159917	159917		-		-	-	0.015	-	-	1.044%
2016-06-06T01:26:59	Jocelyn Larouche	Manual testing	175908	5265000	6	-		-	-	0.043	-	-	3.265%
2016-11-13T02:06:37	Jocelyn Larouche	low 4M	211089	211089		-		-	-	0.020	-	-	1.209%
2017-04-22T17:25:09	Jocelyn Larouche	low 4M	351816	3518160	6	-		-	-	0.050	-	-	3.301%
2017-04-27T04:20:44	Jocelyn Larouche	low 4M	422179	4221790	6	-		-	-	0.060	-	-	3.521%
2017-11-15T22:09:02	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.915%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:07	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.054	-	-
2009-01-04T23:47:00	Sturle Sunde	ghini.ifi	2⁶⁰	2⁶¹		-	-	0.072	-	-
2009-01-07T23:41:00	Sturle Sunde	antonov.ifi	2⁶¹	2⁶²		-	-	0.143	-	-
2013-09-07T11:35:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.458	-	-
2015-03-18T10:56:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.915	-	-
2015-03-18T10:56:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.742	-	-
2015-12-27T16:49:16	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.483	-	-
2016-10-29T15:24:11	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.966	-	-
2019-04-15T13:43:11	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.93	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.266 GHz-days
Estimated T-Level:	2.500

Digits	B1	Curves	Complete	FacMiss
20	11000	50 / 100	0.500	60.501%
25	50000	50 / 280	0.179	83.620%

New Calculation Method

Total ECM effort:	4.266 GHz-days
Estimated T-Level:	2.500

Digits	B1	Complete	FacMiss
20	11000	1.923	14.616%
25	50000	0.178	83.700%
30	250000	0.011	98.884%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		48	4.096
50000	5000000	3723368062513511308520257	2	0.171

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-17T09:11:00	Nathan Slaven	q6600	50000	5000000						3	0.256
2009-11-24T18:08:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.256
2011-08-08T17:03:00	S36049	Wolle5	50000	5000000						3	0.256
2013-04-23T22:11:00	Donna Noble	opt4820	50000	5000000						3	0.256
2015-01-05T14:12:00	arnaud	srv-630	50000	5000000						3	0.256
2015-08-23T06:44:00	Syntony	Geomancer	50000	5000000						3	0.256
2016-02-28T06:07:58	Bruce	Desk6	50000	5000000						3	0.256
2016-06-15T22:19:43	lettp	Home	50000	5000000						3	0.256
2016-09-22T15:29:28	Bruce	Desk6	50000	5000000						3	0.256
2017-03-16T17:34:16	Bruce	Desk6	50000	5000000						3	0.256
2017-10-07T00:57:49	Bruce	Desk6	50000	5000000						3	0.256
2018-02-13T11:43:03	Bruce	Desk6	50000	5000000						3	0.256
2018-07-27T08:47:20	Bruce	Desk6	50000	5000000						3	0.256
2019-10-15T05:55:30	monsted	rootweiler	50000	5000000						3	0.256
2020-01-22T15:58:51	Keysarecool	Boat_Anchor	50000	5000000						3	0.256
2020-01-29T11:43:17	daveward2005	Davy	50000	5000000						3	0.256
2020-02-08T17:36:57	Corey	Computer	50000	5000000	3723368062513511308520257	81.623	2	2		2	0.171

date	userid	compid	res64	spent (GHz-days)
1999-02-21T00:00:00	ANONYMOUS	v4_computers	D38DB6AA6AF6DE19	0.141
2018-04-08T11:11:05	kkmrkkblmbrbk	old	D38DB6AA6AF6DE19	0.141

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 = 2500000, B2 = 125000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 422179, B2 = 4221790 (P-1 stage 2)

B1 = 351816, B2 = 3518160 (P-1 stage 2)

B1 = 175908, B2 = 5265000 (P-1 stage 2)

B1 = 422179 (P-1 stage 1)

B1 = 351816 (P-1 stage 1)

B1 = 130000, B2 = 2632500 (P-1 stage 2)

B1 = 211089 (P-1 stage 1)

B1 = 175908 (P-1 stage 1)

B1 = 159917 (P-1 stage 1)

B1 = 130000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 20000 (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

10⁹

10¹⁰

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