M2607139 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	22.8622	67.6471%	3000000	90000000	0.7784	7.7813%	23.6406	70.1645%	2.5175%
PrimeNet	2⁵⁹	0.0295	62.7119%	11000	200000	0.0021	2.6962%	0.0316	63.7172%	1.0054%
GPU72	2⁶³	0.6122	65.0794%	12000	200000	0.0022	1.5312%	0.6144	65.6141%	0.5347%
Difference	+5	+22.2500	+2.5677%	+2988000	+89800000	+0.7762	+6.2501%	+23.0262	+4.5505%	+4.5505%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2607139	351072073581723979217243983	27	88.182	67328990433905514669 3² × 48527 × 154161578855083	2020-12-18	48527	154161578855083	34,707,578	844,733	1,577,725

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-31T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.238%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.781%
2010-11-16T23:09:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.266%
2010-12-15T18:30:00	markr	tiny	100000	2125000		-		-	-	0.021	-	-	2.472%
2014-10-10T20:28:00	Jocelyn Larouche	Manual testing	124619	124619		-		-	-	0.013	-	-	0.941%
2016-05-18T03:31:30	Jocelyn Larouche	Manual testing	200000	3600000	6	-		-	-	0.039	-	-	3.154%
2017-07-10T01:11:33	Jocelyn Larouche	low 4M	400000	4000000	6	-		-	-	0.060	-	-	3.544%
2019-12-03T14:18:36	masser	Manual testing	2000000	50000000	12	-		-	-	0.464	-	-	6.846%
2019-12-06T20:52:02	BigBrother	Winston	3000000	90000000	12	-		-	-	0.778	-	-	7.781%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.029	-	-
2016-02-23T16:29:17	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.029	-	-
2009-01-27T02:17:00	Sturle Sunde	othello.ifi	2⁶⁰	2⁶¹		-	-	0.059	-	-
2012-06-24T12:11:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.118	-	-
2013-01-14T11:55:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.377	-	-
2015-02-18T11:41:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.753	-	-
2015-02-18T11:41:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.433	-	-
2016-01-15T14:57:03	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.866	-	-
2017-08-24T10:53:49	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.733	-	-
2019-05-13T13:38:10	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.47	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.124 GHz-days
Estimated T-Level:	3.850

Digits	B1	Curves	Complete	FacMiss
20	11000	77 / 100	0.770	46.122%
25	50000	77 / 280	0.275	75.920%

New Calculation Method

Total ECM effort:	7.124 GHz-days
Estimated T-Level:	3.850

Digits	B1	Complete	FacMiss
20	11000	2.962	5.174%
25	50000	0.274	76.032%
30	250000	0.017	98.286%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		75	6.939
50000	5000000	351072073581723979217243983	2	0.185

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-26T15:47:00	Aca Arsov	backo6400	50000	5000000						3	0.278
2010-08-28T20:54:00	Kamil_Górski	thefault	50000	5000000						3	0.278
2012-11-17T02:56:00	Donna Noble	3820v2	50000	5000000						3	0.278
2014-08-17T17:25:00	he4var		50000	5000000						3	0.278
2015-10-17T13:50:08	Viacheslav Chernetskiy	home_E8400	50000	5000000						3	0.278
2016-03-22T19:00:28	Jason U	Server7	50000	5000000						3	0.278
2016-08-17T23:10:00	lettp	Home	50000	5000000						3	0.278
2017-06-09T14:59:50	Bruce	eleven	50000	5000000						3	0.278
2017-10-21T04:59:12	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.278
2018-04-16T20:58:27	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.278
2019-02-23T10:37:54	-Anonymous-		50000	5000000						3	0.278
2020-07-04T20:23:50	GAN	OSB-02	50000	5000000						3	0.278
2020-07-11T15:10:47	GAN	OSK-01	50000	5000000						3	0.278
2020-07-17T19:37:29	mnd9	25836b	50000	5000000						3	0.278
2020-07-23T16:03:18	daveward2005	Davy	50000	5000000						3	0.278
2020-07-30T19:36:52	GAN	XPS	50000	5000000						3	0.278
2020-08-15T08:51:00	lycorn	colab_A	50000	5000000						3	0.278
2020-08-28T15:59:17	nordi	sweet16	50000	5000000						3	0.278
2020-09-10T10:14:13	Oliver Kruse	Krusen-NAS	50000	5000000						7	0.648
2020-10-12T07:47:14	J.R. Allen	lapasus	50000	5000000						7	0.648
2020-11-08T05:57:34	Albrecht Heeffer	R7-3800X	50000	5000000						7	0.648
2020-12-18T15:25:20	Zenzoma	AMD3970X	50000	5000000	351072073581723979217243983	88.182	2	2	7147240267965205	2	0.185

date	userid	compid	res64	spent (GHz-days)
1999-04-02T00:00:00	ANONYMOUS	v4_computers	5899833595D3342A	0.181
2018-06-28T13:19:47	kkmrkkblmbrbk	old	5899833595D3342A	0.181

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 = 90000000 (P-1 stage 2)

B1 = 2000000, B2 = 50000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 2000000 (P-1 stage 1)

B1 = 400000, B2 = 4000000 (P-1 stage 2)

B1 = 400000 (P-1 stage 1)

B1 = 200000, B2 = 3600000 (P-1 stage 2)

B1 = 100000, B2 = 2125000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 124619 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 15000, B2 = 217500 (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