M2685383 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	22.1960	67.6471%	3000000	90000000	0.8668	7.8042%	23.0629	70.1719%	2.5249%
PrimeNet	2⁵⁹	0.0286	62.7119%	12000	220000	0.0026	2.8402%	0.0312	63.7709%	1.0591%
GPU72	2⁶³	0.5943	65.0794%	13000	220000	0.0027	1.6229%	0.5971	65.6461%	0.5667%
Difference	+5	+21.6017	+2.5677%	+2987000	+89780000	+0.8641	+6.1812%	+22.4658	+4.5258%	+4.5258%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2685383	3454434549043963357361	22	71.549	643192153417960 2³ × 5 × 4871 × 3301129919	2020-09-08	4871	3301129919	248.96	20.143	37.620

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.240%
2003-11-28T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.786%
2010-12-22T11:37:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.268%
2010-12-26T02:29:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.371%
2011-02-02T22:45:00	markr	tiny	105000	2283750		-		-	-	0.025	-	-	2.550%
2016-06-16T02:18:33	Jocelyn Larouche	Manual testing	161791	4567500	6	-		-	-	0.045	-	-	3.223%
2016-12-19T18:37:55	Jocelyn Larouche	low 4M	194149	194149		-		-	-	0.022	-	-	1.203%
2017-01-10T10:25:17	Jocelyn Larouche	low 4M	232978	232978		-		-	-	0.026	-	-	1.319%
2017-04-04T20:17:36	Jocelyn Larouche	low 4M	335487	3354870	6	-		-	-	0.056	-	-	3.344%
2018-09-03T21:22:24	Jocelyn Larouche	low 4M	486584	486584		-		-	-	0.054	-	-	1.857%
2019-07-05T23:33:42	BigBrother	Winston	3000000	90000000	12	-		-	-	0.867	-	-	7.804%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:19	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.057	-	-
2009-01-31T16:11:00	Sturle Sunde	gerle.ifi	2⁶⁰	2⁶¹		-	-	0.057	-	-
2012-05-09T13:02:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.114	-	-
2013-01-14T12:26:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.366	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.731	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.391	-	-
2016-01-26T10:48:52	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.783	-	-
2017-09-13T08:55:33	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.565	-	-
2019-04-29T13:20:16	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.13	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.864 GHz-days
Estimated T-Level:	2.350

Digits	B1	Curves	Complete	FacMiss
20	11000	47 / 100	0.470	62.353%
25	50000	47 / 280	0.168	84.522%

New Calculation Method

Total ECM effort:	4.864 GHz-days
Estimated T-Level:	2.350

Digits	B1	Complete	FacMiss
20	11000	1.516	21.956%
25	50000	0.137	87.195%
30	250000	0.008	99.160%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		45	4.657
50000	5000000	3454434549043963357361	2	0.207

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-08T03:33:00	Never Odd Or Even	C_Quad	50000	5000000						3	0.310
2010-07-31T11:10:00	Lupo	yorick	50000	5000000						3	0.310
2012-12-18T05:43:00	oodaira	Linux01	50000	5000000						3	0.310
2014-12-31T16:57:00	arnaud	SPR05	50000	5000000						3	0.310
2016-02-04T21:10:07	JShaft	fw	50000	5000000						3	0.310
2016-04-21T11:51:53	cherridge	Home	50000	5000000						3	0.310
2016-10-12T00:55:36	Ensigma	vps_sing	50000	5000000						3	0.310
2017-07-09T12:50:39	Bruce	eleven	50000	5000000						3	0.310
2017-11-16T12:14:39	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.310
2018-06-14T05:49:25	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.310
2019-08-30T04:28:27	prime235711	prime235711	50000	5000000						3	0.310
2020-07-23T05:27:20	Ahmed Azhad	c5.4xlarge.azf	50000	5000000						3	0.310
2020-07-30T02:07:51	GAN	PG-HP	50000	5000000						3	0.310
2020-08-07T08:18:57	Oliver Kruse	Krusen-NAS	50000	5000000						3	0.310
2020-08-14T23:12:36	IanGlencross	glenx24	50000	5000000						3	0.310
2020-09-08T10:07:45	daveward2005	Dave2	50000	5000000	3454434549043963357361	71.549	2	2		2	0.207

date	userid	compid	res64	spent (GHz-days)
1999-05-09T00:00:00	ANONYMOUS	v4_computers	13539E9EB2D8EED3	0.207
2018-07-27T16:29:11	kkmrkkblmbrbk	old	13539E9EB2D8EED3	0.207

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 = 335487, B2 = 3354870 (P-1 stage 2)

B1 = 486584 (P-1 stage 1)

B1 = 161791, B2 = 4567500 (P-1 stage 2)

B1 = 335487 (P-1 stage 1)

B1 = 232978 (P-1 stage 1)

B1 = 105000, B2 = 2283750 (P-1 stage 2)

B1 = 194149 (P-1 stage 1)

B1 = 161791 (P-1 stage 1)

B1 = 105000 (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)

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