M2361581 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	25.2394	67.6471%	3000000	100000000	0.8115	7.8343%	26.0509	70.1817%	2.5346%
PrimeNet	2⁵⁹	0.0325	62.7119%	10000	170000	0.0018	2.4721%	0.0344	63.6337%	0.9218%
GPU72	2⁶³	0.6758	65.0794%	10000	140000	0.0017	1.2706%	0.6775	65.5231%	0.4437%
Difference	+5	+24.5636	+2.5677%	+2990000	+99860000	+0.8099	+6.5637%	+25.3734	+4.6586%	+4.6586%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2361581	1419494835824907029887	22	70.266	300539095594203 3 × 19 × 5272615712179	2021-01-28	19	5272615712179	113.08	28,139	52,556

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-21T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.231%
2010-11-03T21:25:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.260%
2010-12-23T23:07:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.682%
2011-01-22T22:53:00	Oscar Östlin		90000	1822500		-		-	-	0.018	-	-	2.297%
2014-08-07T10:52:00	Jocelyn Larouche	Manual testing	117179	117179		-		-	-	0.011	-	-	0.893%
2014-10-22T23:53:00	Jocelyn Larouche	Manual testing	144358	144358		-		-	-	0.014	-	-	1.004%
2015-08-25T02:37:00	mikr	MSI	3000000	100000000		-		-	-	0.812	-	-	7.834%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.033	-	-
2016-02-23T16:29:12	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.033	-	-
2009-01-11T11:00:00	Sturle Sunde	ghini.ifi	2⁶⁰	2⁶¹		-	-	0.065	-	-
2012-05-30T12:44:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.130	-	-
2013-01-23T08:26:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.416	-	-
2015-03-09T12:35:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.831	-	-
2015-03-09T12:35:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.582	-	-
2015-10-29T11:36:26	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.164	-	-
2017-06-13T16:34:55	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.329	-	-
2019-04-22T13:11:34	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.66	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	10.480 GHz-days
Estimated T-Level:	22.107

Digits	B1	Curves	Complete	FacMiss
20	11000	118 / 100	1.180	30.546%
25	50000	118 / 280	0.421	65.561%

New Calculation Method

Total ECM effort:	10.480 GHz-days
Estimated T-Level:	22.107

Digits	B1	Complete	FacMiss
20	11000	3.806	2.223%
25	50000	0.344	70.891%
30	250000	0.021	97.904%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		116	10.30
50000	5000000	1419494835824907029887	2	0.178

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-27T20:53:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.266
2010-02-03T22:25:00	James Classen	towerofart	50000	5000000						3	0.266
2012-01-06T01:54:00	S36049	Wolle5	50000	5000000						3	0.266
2013-11-03T12:21:00	arnaud	srv-630	50000	5000000						3	0.266
2015-06-14T15:17:00	guru	w6	50000	5000000						3	0.266
2016-02-18T09:13:59	Sintax	cloud	50000	5000000						3	0.266
2016-05-13T03:54:47	Bruce	Desk6	50000	5000000						3	0.266
2016-09-04T02:44:00	Bruce	Desk6	50000	5000000						3	0.266
2017-03-07T06:09:32	Bruce	Desk6	50000	5000000						3	0.266
2017-10-13T19:35:12	Bruce	Desk6	50000	5000000						3	0.266
2018-03-05T12:52:19	Bruce	Desk6	50000	5000000						3	0.266
2018-09-09T03:51:09	Bruce	Desk6	50000	5000000						3	0.266
2020-03-19T22:05:08	Nesowa	entropy_generator_2	50000	5000000						3	0.266
2020-03-30T02:28:51	Alvin Bunk	BADCAT	50000	5000000						3	0.266
2020-04-11T18:08:57	Oliver Kruse	Threadripper-PC	50000	5000000						3	0.266
2020-04-23T08:33:49	Oliver Kruse	IOS-1	50000	5000000						3	0.266
2020-04-30T11:15:12	mnd9	221Rb	50000	5000000						3	0.266
2020-05-11T20:33:44	mnd9	office2	50000	5000000						3	0.266
2020-05-27T10:30:13	Yxinity	Olga	50000	5000000						3	0.266
2020-06-15T02:03:39	J.R. Allen	lapacer-kubuntu	50000	5000000						3	0.266
2020-06-29T09:20:46	GAN	KL-SCH04	50000	5000000						3	0.266
2020-07-06T05:06:46	mnd9	libproj	50000	5000000						3	0.266
2020-07-12T16:25:25	mnd9	25836b	50000	5000000						3	0.266
2020-07-18T03:54:52	GAN	PG-MS	50000	5000000						3	0.266
2020-07-31T11:38:57	daveward2005	Davy	50000	5000000						3	0.266
2020-08-05T01:27:42	mnd9	25836b	50000	5000000						3	0.266
2020-08-08T00:15:35	GAN	LMS-13	50000	5000000						3	0.266
2020-08-16T23:15:20	Ensigma		50000	5000000						7	0.622
2020-09-17T07:49:20	daveward2005	Dave2	50000	5000000						7	0.622
2020-10-17T10:29:31	mnd9	75204	50000	5000000						7	0.622
2020-11-19T16:33:29	mnd9	27016b	50000	5000000						7	0.622
2020-12-27T01:55:42	Gerry Snyder	Gerry-Workstation	50000	5000000						7	0.622
2021-01-28T05:54:29	daveward2005	Dave2	50000	5000000	1419494835824907029887	70.266	2	2	2098719507543933	2	0.178

date	userid	compid	res64	spent (GHz-days)
2015-11-15T03:19:14	MadPoo	Manual testing	A796FE5EA25EE094	0.160

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 = 100000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 90000, B2 = 1822500 (P-1 stage 2)

B1 = 144358 (P-1 stage 1)

B1 = 117179 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 75011 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10⁰

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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