M2540113 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	23.4654	67.6471%	3000000	135000000	1.0250	8.2616%	24.4905	70.3199%	2.6729%
PrimeNet	2⁵⁹	0.0302	62.7119%	11000	200000	0.0021	2.6833%	0.0324	63.7124%	1.0006%
GPU72	2⁶³	0.6283	65.0794%	12000	180000	0.0021	1.4769%	0.6305	65.5951%	0.5157%
Difference	+5	+22.8371	+2.5677%	+2988000	+134820000	+1.0229	+6.7847%	+23.8600	+4.7248%	+4.7248%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2540113	312234113144836721705924879	27	88.013	61460673825305551703 19 × 5903 × 547987854750979	2020-07-09	5903	547987854750979	32,813,704	3,002,715	5,608,235

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-23T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.236%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	198750		-		-	-	0.003	-	-	0.755%
2010-12-19T21:42:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.265%
2011-01-02T14:09:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.366%
2011-01-07T22:30:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.530%
2011-04-05T19:27:00	James Heinrich	WHS	300000	8000000		-		-	-	0.072	-	-	3.958%
2018-08-11T22:21:47	Jocelyn Larouche	low 4M	600000	6000000	6	-		-	-	0.090	-	-	4.048%
2018-08-30T20:06:57	mikr	MSI	3000000	135000000	12	-		-	-	1.025	-	-	8.262%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
2016-02-23T16:29:16	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.030	-	-
2009-02-04T06:24:00	Sturle Sunde	czerny.ifi	2⁶⁰	2⁶¹		-	-	0.060	-	-
2012-06-15T09:42:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.121	-	-
2013-01-23T08:30:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.386	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.773	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.471	-	-
2015-11-08T21:03:13	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.942	-	-
2017-08-08T13:42:10	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.884	-	-
2019-04-29T13:20:21	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.77	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.147 GHz-days
Estimated T-Level:	2.250

Digits	B1	Curves	Complete	FacMiss
20	11000	45 / 100	0.450	63.619%
25	50000	45 / 280	0.161	85.129%

New Calculation Method

Total ECM effort:	4.147 GHz-days
Estimated T-Level:	2.250

Digits	B1	Complete	FacMiss
20	11000	1.452	23.419%
25	50000	0.131	87.705%
30	250000	0.008	99.195%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		43	3.963
50000	5000000	312234113144836721705924879	2	0.184

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-10-03T01:03:00	Rob_Dee	twopc	50000	5000000						1	0.092
2009-10-11T01:03:00	James Hintz	08_091909	50000	5000000						3	0.276
2011-01-01T23:38:00	James Hintz	ryan	50000	5000000						3	0.276
2013-04-05T12:52:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.276
2015-03-10T10:14:00	Bruce	desk16	50000	5000000						3	0.276
2016-02-04T12:04:03	Bruce	Desk8	50000	5000000						3	0.276
2016-04-18T07:51:17	AnthonyRais		50000	5000000						3	0.276
2016-09-23T11:56:14	lettp	Home	50000	5000000						3	0.276
2017-06-30T03:09:53	Sebastian Hornbostel	V2	50000	5000000						3	0.276
2017-10-28T17:43:01	Sebastian Hornbostel	V2	50000	5000000						3	0.276
2018-04-27T10:06:23	Palantsevich	OfficeB01	50000	5000000						3	0.276
2019-02-27T09:53:23	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.276
2020-06-08T16:00:15	mnd9	25836b	50000	5000000						3	0.276
2020-06-25T06:38:11	daveward2005	MW	50000	5000000						3	0.276
2020-07-03T05:47:51	lycorn	colab_A	50000	5000000						3	0.276
2020-07-09T19:23:42	GAN	LMS-03	50000	5000000	312234113144836721705924879	88.013	2	2	1206125597064985	2	0.184

date	userid	compid	res64	spent (GHz-days)
1999-06-15T00:00:00	ANONYMOUS	v4_computers	8659E306099B6F79	0.176
2018-06-09T17:56:46	kkmrkkblmbrbk	old	8659E306099B6F79	0.176

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 = 3000000, B2 = 135000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 600000, B2 = 6000000 (P-1 stage 2)

B1 = 300000, B2 = 8000000 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 198750 (P-1 stage 2)

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)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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