M2684273 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	22.2052	67.6471%	3000000	90000000	0.8668	7.8039%	23.0720	70.1718%	2.5248%
PrimeNet	2⁵⁹	0.0286	62.7119%	12000	220000	0.0026	2.8400%	0.0312	63.7709%	1.0590%
GPU72	2⁶³	0.5946	65.0794%	13000	220000	0.0027	1.6228%	0.5973	65.6461%	0.5667%
Difference	+5	+21.6106	+2.5677%	+2987000	+89780000	+0.8641	+6.1810%	+22.4747	+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
2684273	9718036342990214329897	22	73.041	1810180324987476 2² × 3 × 13 × 257 × 45150661603	2020-09-07	257	45150661603	1,042.1	275.49	514.55

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%
2010-12-21T22:27:00	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%
2011-02-03T09:16:00	markr	tiny	105000	2283750		-		-	-	0.025	-	-	2.550%
2016-06-15T12:00:40	Jocelyn Larouche	Manual testing	161802	4567500	6	-		-	-	0.045	-	-	3.222%
2016-12-19T18:37:55	Jocelyn Larouche	low 4M	194162	194162		-		-	-	0.022	-	-	1.203%
2017-01-10T10:25:17	Jocelyn Larouche	low 4M	232994	232994		-		-	-	0.026	-	-	1.319%
2017-04-07T19:41:22	Jocelyn Larouche	low 4M	335510	3355100	6	-		-	-	0.056	-	-	3.344%
2018-09-03T21:22:24	Jocelyn Larouche	low 4M	486612	486612		-		-	-	0.054	-	-	1.857%
2019-07-04T23:14:29	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	-	-
2009-01-31T02:54:00	Sturle Sunde	goober.ifi	2⁶⁰	2⁶¹		-	-	0.057	-	-
2012-05-11T05:01:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.114	-	-
2013-01-23T08:31:00	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		-	-	1.392	-	-
2016-01-26T10:48:52	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.784	-	-
2017-09-13T08:55:33	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.568	-	-
2019-05-06T12:23:21	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.14	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.174 GHz-days
Estimated T-Level:	2.500

Digits	B1	Curves	Complete	FacMiss
20	11000	50 / 100	0.500	60.501%
25	50000	50 / 280	0.179	83.620%

New Calculation Method

Total ECM effort:	5.174 GHz-days
Estimated T-Level:	2.500

Digits	B1	Complete	FacMiss
20	11000	1.613	19.931%
25	50000	0.146	86.435%
30	250000	0.009	99.106%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		45	4.657
50000	5000000	9718036342990214329897	5	0.517

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-16T05:04:00	wuxiao	DNE_Black_Sheep	50000	5000000						3	0.310
2010-08-01T08:28:00	Kamil_Górski	thefault	50000	5000000						3	0.310
2012-12-19T04:23:00	Smurgs	Praca	50000	5000000						3	0.310
2014-12-28T15:15:00	arnaud	srv-630	50000	5000000						3	0.310
2016-01-29T23:32:40	Jason U	Server7	50000	5000000						3	0.310
2016-04-19T11:15:28	AnthonyRais	Main	50000	5000000						3	0.310
2016-10-12T20:29:56	S36049	Wolle5	50000	5000000						3	0.310
2017-07-09T13:38:09	AnthonyRais	Win10Test	50000	5000000						3	0.310
2017-11-16T00:50:56	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.310
2018-06-12T16:30:59	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.310
2019-08-28T22:30:14	prime235711	prime235711	50000	5000000						3	0.310
2020-07-23T10:57:44	mnd9	libproj	50000	5000000						3	0.310
2020-07-29T19:06:36	GAN	LMS-13	50000	5000000						3	0.310
2020-08-06T17:09:24	rextherunt	ice	50000	5000000						3	0.310
2020-08-15T01:52:36	mnd9	libproj	50000	5000000						3	0.310
2020-09-07T16:14:34	daveward2005	MW	50000	5000000	9718036342990214329897	73.041	5	2		5	0.517

date	userid	compid	res64	spent (GHz-days)
1999-04-23T00:00:00	ANONYMOUS	v4_computers	A5EC264FF0F4B4AE	0.207
2018-07-27T07:06:12	kkmrkkblmbrbk	old	A5EC264FF0F4B4AE	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 = 335510, B2 = 3355100 (P-1 stage 2)

B1 = 486612 (P-1 stage 1)

B1 = 161802, B2 = 4567500 (P-1 stage 2)

B1 = 335510 (P-1 stage 1)

B1 = 232994 (P-1 stage 1)

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

B1 = 194162 (P-1 stage 1)

B1 = 161802 (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)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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