M2123087 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	28.0746	67.6471%	2500000	125000000	0.8746	7.9070%	28.9493	70.2052%	2.5581%
PrimeNet	2⁵⁸	0.0181	62.0690%	9000	160000	0.0016	2.6833%	0.0197	63.0868%	1.0178%
GPU72	2⁶²	0.2894	64.5161%	10000	140000	0.0016	1.4545%	0.2910	65.0323%	0.5161%
Difference	+6	+27.7853	+3.1309%	+2490000	+124860000	+0.8730	+6.4524%	+28.6583	+5.1729%	+5.1729%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2123087	7421524939997930234177	22	72.652	1747814606749024 2⁵ × 11 × 1523 × 3260264219	2020-10-26	1523	3260264219	755.09	16.935	31.629

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-08-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.224%
2009-08-03T14:50:00	harlee	P4_2600	20000	265000		-		-	-	0.003	-	-	0.884%
2011-01-01T00:56:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.352%
2011-01-11T22:55:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.511%
2011-01-24T09:54:00	James Heinrich	i7-920	140000	3045000		-		-	-	0.028	-	-	2.778%
2016-06-24T05:32:52	Jocelyn Larouche	Manual testing	210000	6090000	12	-		-	-	0.051	-	-	3.462%
2017-08-19T15:19:13	Jocelyn Larouche	low 4M	420000	4200000	6	-		-	-	0.060	-	-	3.510%
2017-08-28T16:38:41	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.907%
2017-08-30T00:32:07	Jocelyn Larouche	low 4M	504000	5040000	6	-		-	-	0.072	-	-	3.736%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:05	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.054	-	-
2009-01-03T19:58:00	Sturle Sunde	gobi.ifi	2⁶⁰	2⁶¹		-	-	0.072	-	-
2012-04-02T20:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.145	-	-
2013-09-06T08:31:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.462	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.925	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.760	-	-
2015-10-26T20:11:48	omylist	Manual testing	2⁶⁵	2⁶⁶		-	-	3.520	-	-
2016-10-15T17:13:26	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.040	-	-
2019-05-06T12:23:36	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	14.08	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	11.238 GHz-days
Estimated T-Level:	22.321

Digits	B1	Curves	Complete	FacMiss
20	11000	130 / 100	1.300	27.075%
25	50000	130 / 280	0.464	62.806%

New Calculation Method

Total ECM effort:	11.238 GHz-days
Estimated T-Level:	22.321

Digits	B1	Complete	FacMiss
20	11000	4.217	1.475%
25	50000	0.382	68.234%
30	250000	0.024	97.666%
35	1000000	0.001	99.891%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		128	10.91
50000	5000000	7421524939997930234177	1	0.085
76620	24176890		1	0.246

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-16T06:17:00	alan145	Bear4	50000	5000000						3	0.256
2009-11-20T06:04:00	ANONYMOUS	fn-asterisk	50000	5000000						3	0.256
2011-07-17T23:01:00	S36049	Wolle5	50000	5000000						3	0.256
2013-04-16T17:16:00	Xyzzy	J	50000	5000000						3	0.256
2014-11-26T03:25:00	thefourseasons	dawgs	50000	5000000						3	0.256
2015-08-08T09:15:00	guru	w1	50000	5000000						3	0.256
2016-02-24T11:42:45	Bruce	Desk6	50000	5000000						3	0.256
2016-06-06T00:25:32	Jason U	Server7	50000	5000000						3	0.256
2016-08-28T20:01:11	Bruce	test	50000	5000000						3	0.256
2017-02-28T06:35:17	Bruce	Desk6	50000	5000000						3	0.256
2017-09-11T00:04:33	Bruce	Desk6	50000	5000000						3	0.256
2018-01-25T17:23:11	Bruce	Desk6	50000	5000000						3	0.256
2018-07-09T22:16:13	Bruce	Desk6	50000	5000000						3	0.256
2019-08-17T05:45:04	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.256
2020-01-16T23:14:01	IEFBR14	MK1	50000	5000000						3	0.256
2020-01-22T13:21:27	Sergey Nosov	TS140-02	50000	5000000						3	0.256
2020-01-29T09:44:08	Sergey Nosov	TS140-02	50000	5000000						3	0.256
2020-02-07T21:30:20	mnd9	25836b	50000	5000000						3	0.256
2020-02-15T10:56:12	mnd9	libproj	50000	5000000						3	0.256
2020-02-22T16:02:15	Keysarecool	HPLaptop	50000	5000000						3	0.256
2020-02-29T07:29:29	mnd9	75211backdoorb	50000	5000000						3	0.256
2020-03-09T01:55:02	Nesowa	6700T	50000	5000000						3	0.256
2020-03-14T01:57:11	mnd9	75211backdoorb	50000	5000000						3	0.256
2020-03-21T14:21:09	IanGlencross	glenx24	50000	5000000						3	0.256
2020-04-03T11:59:25	mnd9	office	50000	5000000						3	0.256
2020-04-17T07:48:23	mnd9	libproj	50000	5000000						3	0.256
2020-04-26T11:29:54	Bommer	3770K	50000	5000000						3	0.256
2020-05-04T06:22:27	EricP	Cannonfodder	50000	5000000						3	0.256
2020-05-15T20:39:33	mnd9	eileen	50000	5000000						3	0.256
2020-06-02T21:42:39	lycorn	colab_A	50000	5000000						3	0.256
2020-06-22T17:22:35	LaurV	3tits	50000	5000000						3	0.256
2020-07-01T13:19:47	GAN	LMS-18	50000	5000000						3	0.256
2020-07-08T17:33:15	mnd9	libproj	50000	5000000						3	0.256
2020-07-16T10:11:35	Leo Custodio	GCP-013	50000	5000000						3	0.256
2020-07-22T15:18:45	Claude Portenier	Petit-Idiot	50000	5000000						3	0.256
2020-07-27T02:39:06	GAN	XPS	50000	5000000						3	0.256
2020-08-03T04:46:54	GAN	LMS-01	50000	5000000						3	0.256
2020-08-10T23:26:23	lycorn	colab_S	50000	5000000						3	0.256
2020-08-28T06:50:24	nordi	sweet16	50000	5000000						7	0.597
2020-09-30T01:36:00	daveward2005	Dave2	50000	5000000						7	0.597
2020-10-26T13:19:06	nordi	sweet16	50000	5000000	7421524939997930234177	72.652	1	2	4415077578512903	1	0.085
2020-11-09T21:38:28	Bruno Victal	Manual testing	76620	24176890						1	0.246

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	B7737D798712375A	0.140
2018-04-04T16:00:51	kkmrkkblmbrbk	old	B7737D798712375A	0.140

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 = 504000, B2 = 5040000 (P-1 stage 2)

B1 = 420000, B2 = 4200000 (P-1 stage 2)

B1 = 210000, B2 = 6090000 (P-1 stage 2)

B1 = 504000 (P-1 stage 1)

B1 = 420000 (P-1 stage 1)

B1 = 140000, B2 = 3045000 (P-1 stage 2)

B1 = 210000 (P-1 stage 1)

B1 = 140000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 265000 (P-1 stage 2)

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