M2783687 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	21.4122	67.6471%	3000000	90000000	0.8668	7.8321%	22.2790	70.1810%	2.5339%
PrimeNet	2⁵⁹	0.0276	62.7119%	12000	220000	0.0026	2.8588%	0.0302	63.7778%	1.0660%
GPU72	2⁶³	0.5733	65.0794%	15000	240000	0.0031	1.7479%	0.5764	65.6897%	0.6104%
Difference	+5	+20.8389	+2.5677%	+2985000	+89760000	+0.8638	+6.0842%	+21.7026	+4.4912%	+4.4912%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2783687	3802112810550386161441	22	71.687	682927500568560 2⁴ × 3 × 5 × 13 × 23 × 67 × 142042193	2021-01-31	67	142042193	321.24	0.8667	1.6187

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-17T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.242%
2010-11-11T04:19:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.002	-	-	0.211%
2010-11-25T20:06:00	markr	tiny	100000	2075000		-		-	-	0.023	-	-	2.483%
2014-10-28T23:25:00	Jocelyn Larouche	Manual testing	123057	123057		-		-	-	0.014	-	-	0.946%
2016-05-03T01:41:40	Jocelyn Larouche	Manual testing	200000	3600000	6	-		-	-	0.043	-	-	3.183%
2017-07-20T22:03:20	Jocelyn Larouche	low 4M	400000	4000000	6	-		-	-	0.067	-	-	3.575%
2019-11-14T10:43:13	BigBrother	Winston	3000000	90000000	12	-		-	-	0.867	-	-	7.832%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:21	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.055	-	-
2009-01-28T05:36:00	Sturle Sunde	gimba.ifi	2⁶⁰	2⁶¹		-	-	0.055	-	-
2012-04-01T07:57:00	Grant McCracken	home	2⁶¹	2⁶²		-	-	0.110	-	-
2013-01-14T12:31:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.353	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.705	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.342	-	-
2016-02-08T11:13:52	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.684	-	-
2017-10-16T21:21:14	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.369	-	-
2019-02-25T02:38:33	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.74	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.974 GHz-days
Estimated T-Level:	3.350

Digits	B1	Curves	Complete	FacMiss
20	11000	67 / 100	0.670	50.999%
25	50000	67 / 280	0.239	78.685%

New Calculation Method

Total ECM effort:	6.974 GHz-days
Estimated T-Level:	3.350

Digits	B1	Complete	FacMiss
20	11000	2.161	11.518%
25	50000	0.195	82.256%
30	250000	0.012	98.804%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		61	6.349
50000	5000000	3802112810550386161441	6	0.625

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-22T11:39:00	Lukasz Wrobel	UNIX_05	50000	5000000						3	0.312
2010-09-27T04:39:00	wallu		50000	5000000						3	0.312
2013-04-01T16:53:00	Jacques MOLNE	Old_faithfull	50000	5000000						3	0.312
2015-03-17T22:44:00	Bruce	desk16	50000	5000000						3	0.312
2016-02-15T07:07:29	Sintax	cloud2	50000	5000000						3	0.312
2016-05-25T01:33:02	lettp	Home	50000	5000000						3	0.312
2017-02-07T07:29:18	Marius Zens	KBWR_TV3	50000	5000000						3	0.312
2017-08-07T22:31:20	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.312
2018-01-11T19:23:34	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.312
2018-11-03T16:51:38	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.312
2020-08-11T03:44:37	GAN	LMS-15	50000	5000000						3	0.312
2020-08-27T15:20:02	M. R. Mayer	nimbus	50000	5000000						7	0.729
2020-09-30T16:52:41	daveward2005	Dave2	50000	5000000						7	0.729
2020-10-26T08:35:30	mnd9	75204	50000	5000000						7	0.729
2021-01-05T00:23:50	rextherunt	ice	50000	5000000						7	0.729
2021-01-31T04:42:13	daveward2005	Davy	50000	5000000	3802112810550386161441	71.687	6	2	8865422939430890	6	0.625

date	userid	compid	res64	spent (GHz-days)
1999-05-30T00:00:00	ANONYMOUS	v4_computers	6B1D7EC88C5A1E4E	0.215
2018-08-26T08:13:04	kkmrkkblmbrbk	old	6B1D7EC88C5A1E4E	0.215

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 = 3000000 (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 = 2075000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 123057 (P-1 stage 1)

B1 = 100000 (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

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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