M2627789 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	22.6825	67.6471%	8000000	250000000	2.3725	9.6694%	25.0551	70.7754%	3.1283%
PrimeNet	2⁵⁹	0.0292	62.7119%	11000	200000	0.0024	2.7002%	0.0316	63.7187%	1.0068%
GPU72	2⁶³	0.6074	65.0794%	13000	200000	0.0026	1.5722%	0.6100	65.6284%	0.5490%
Difference	+5	+22.0752	+2.5677%	+7987000	+249800000	+2.3699	+8.0972%	+24.4451	+5.1470%	+5.1470%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2627789	996232075816789713059201	24	79.721	189557090736126400 2⁶ × 5² × 7 × 16924740244297	2021-03-10	64	16924740244297	87,536	103,269	192,878

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	-	-	0.782%
2010-12-21T22:27:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.267%
2010-12-26T02:29:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.369%
2011-01-20T22:46:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.534%
2011-02-28T05:06:00	James Heinrich	i7-920	300000	8000000		-		-	-	0.081	-	-	3.975%
2018-07-27T08:56:21	mikr	S068	8000000	250000000	12	-		-	-	2.373	-	-	9.669%
2019-10-21T15:48:25	masser	Manual testing	2630000	26300000	12	-		-	-	0.439	-	-	6.222%

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	-	-
2009-02-13T16:21:00	Sturle Sunde	ghibu.ifi	2⁶⁰	2⁶¹		-	-	0.058	-	-
2012-06-16T11:34:00	Grant McCracken	home	2⁶¹	2⁶²		-	-	0.117	-	-
2013-01-14T11:57:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.374	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.747	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.422	-	-
2016-01-18T09:58:45	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.844	-	-
2017-09-01T23:24:07	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.687	-	-
2019-04-01T13:34:42	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.37	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	10.005 GHz-days
Estimated T-Level:	4.850

Digits	B1	Curves	Complete	FacMiss
20	11000	97 / 100	0.970	37.724%
25	50000	97 / 280	0.346	70.677%

New Calculation Method

Total ECM effort:	10.005 GHz-days
Estimated T-Level:	4.850

Digits	B1	Complete	FacMiss
20	11000	3.129	4.376%
25	50000	0.283	75.367%
30	250000	0.017	98.274%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		93	9.59
50000	5000000	996232075816789713059201	4	0.413

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-28T16:44:00	Smurgs	Praca	50000	5000000						3	0.309
2010-06-17T02:43:00	Lupo	yorick	50000	5000000						3	0.309
2012-11-30T00:12:00	Donna Noble	PH2-940-v3-MVB	50000	5000000						3	0.309
2014-10-02T11:39:00	KAMCOBILL	PC20	50000	5000000						3	0.309
2015-12-14T17:51:45	guru	w1	50000	5000000						3	0.309
2016-04-06T09:28:46	jwdenney	johndenney	50000	5000000						3	0.309
2016-08-27T23:10:18	Ensigma	vps_of_jj	50000	5000000						3	0.309
2017-06-20T22:03:14	Daniel Koszta	_	50000	5000000						3	0.309
2017-10-28T07:08:12	Sebastian Hornbostel	V2	50000	5000000						3	0.309
2018-04-27T19:58:35	deo2016	VPS_001	50000	5000000						3	0.309
2019-03-10T04:04:45	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.309
2020-07-10T06:17:33	Nesowa	6700T	50000	5000000						3	0.309
2020-07-16T09:40:59	GAN	PG-HP	50000	5000000						3	0.309
2020-07-22T05:54:35	GAN	LMS-18	50000	5000000						3	0.309
2020-07-28T20:12:47	GAN	LMS-18	50000	5000000						3	0.309
2020-08-05T08:26:15	J.R. Allen	lapasus	50000	5000000						3	0.309
2020-08-13T11:48:56	GAN	LMS-11	50000	5000000						3	0.309
2020-09-06T00:58:02	GAN	KL-SCH05	50000	5000000						7	0.722
2020-10-06T02:53:48	MarkS	desktop-i7	50000	5000000						7	0.722
2020-11-05T22:32:55	Nesowa	entropy_generator_2	50000	5000000						7	0.722
2020-12-09T00:33:28	rextherunt	ice	50000	5000000						7	0.722
2021-01-10T03:23:10	daveward2005	Davy	50000	5000000						7	0.722
2021-02-08T18:38:27	Zenzoma	AMD3970X	50000	5000000						7	0.722
2021-03-10T22:06:37	daveward2005	Dave2	50000	5000000	996232075816789713059201	79.721	4	2	1216166677928541	4	0.413

date	userid	compid	res64	spent (GHz-days)
1999-04-02T00:00:00	ANONYMOUS	v4_computers	17260CB5CE97B9__	0.203
1999-08-22T00:00:00	ANONYMOUS	v4_computers	2824CD9A974105__	0.203

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 = 8000000, B2 = 250000000 (P-1 stage 2)

B1 = 8000000 (P-1 stage 1)

B1 = 2630000, B2 = 26300000 (P-1 stage 2)

B1 = 2630000 (P-1 stage 1)

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

B1 = 300000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (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)

10⁰

10¹

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10³

10⁴

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10⁶

10⁷

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10¹

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10³

10⁴

10⁵

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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