M2680241 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	22.2386	67.6471%	2000000	50000000	0.5169	6.8661%	22.7555	69.8684%	2.2214%
PrimeNet	2⁵⁹	0.0287	62.7119%	12000	220000	0.0026	2.8393%	0.0313	63.7706%	1.0587%
GPU72	2⁶³	0.5955	65.0794%	13000	220000	0.0027	1.6223%	0.5982	65.6459%	0.5665%
Difference	+5	+21.6432	+2.5677%	+1987000	+49780000	+0.5141	+5.2438%	+22.1573	+4.2226%	+4.2226%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2680241	3208200092868214522031	22	71.442	598490973921415 5 × 1303 × 91863541661	2020-09-02	1303	91863541661	319.54	560.52	1,046.9

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%
2010-11-20T12:24:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.268%
2010-12-05T18:17:00	markr	tiny	105000	2283750		-		-	-	0.025	-	-	2.549%
2016-06-14T05:07:20	Jocelyn Larouche	Manual testing	151841	4567500	6	-		-	-	0.044	-	-	3.186%
2016-12-17T04:47:50	Jocelyn Larouche	low 4M	182209	182209		-		-	-	0.020	-	-	1.163%
2016-12-29T21:56:33	Jocelyn Larouche	low 4M	218650	218650		-		-	-	0.024	-	-	1.277%
2017-03-03T01:10:49	Jocelyn Larouche	low 4M	314856	3148560	6	-		-	-	0.053	-	-	3.267%
2018-02-20T11:49:00	Jocelyn Larouche	low 4M	377827	377827		-		-	-	0.042	-	-	1.660%
2018-08-23T10:06:01	Jocelyn Larouche	low 4M	907827	1815654	6	-		-	-	0.107	-	-	3.061%
2018-08-29T01:29:31	Jocelyn Larouche	low 4M	907827	3631308	6	-		-	-	0.118	-	-	3.734%
2019-11-16T14:17:39	masser	Manual testing	2000000	50000000	12	-		-	-	0.517	-	-	6.866%

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	-	-
2009-01-31T17:15:00	Sturle Sunde	krebs.ifi	2⁶⁰	2⁶¹		-	-	0.057	-	-
2012-05-18T02:28:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.115	-	-
2013-01-14T12:25:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.366	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.733	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.394	-	-
2016-01-25T14:29:40	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.788	-	-
2017-09-13T08:55:32	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.576	-	-
2019-05-27T13:36:55	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.15	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.759 GHz-days
Estimated T-Level:	2.300

Digits	B1	Curves	Complete	FacMiss
20	11000	46 / 100	0.460	62.982%
25	50000	46 / 280	0.164	84.825%

New Calculation Method

Total ECM effort:	4.759 GHz-days
Estimated T-Level:	2.300

Digits	B1	Complete	FacMiss
20	11000	1.484	22.676%
25	50000	0.134	87.449%
30	250000	0.008	99.178%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		45	4.656
50000	5000000	3208200092868214522031	1	0.103

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-07T01:13:00	Never Odd Or Even	T_Quad	50000	5000000						3	0.310
2010-07-25T03:39:00	ANONYMOUS		50000	5000000						3	0.310
2012-12-11T12:54:00	Lukasz Wrobel	i-4	50000	5000000						3	0.310
2014-12-23T19:08:00	arnaud	srv-630	50000	5000000						3	0.310
2016-03-29T05:47:39	Conductor	Lena	50000	5000000						3	0.310
2016-04-18T09:35:54	AnthonyRais		50000	5000000						3	0.310
2016-10-12T11:55:17	Conductor	Manual testing	50000	5000000						3	0.310
2016-10-15T19:32:22	lettp	Home	50000	5000000						3	0.310
2017-11-13T17:21:33	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.310
2018-06-08T20:02:46	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.310
2019-08-21T16:39:44	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.310
2020-07-22T14:12:27	mnd9	libproj	50000	5000000						3	0.310
2020-07-28T14:43:42	GAN	LMS-06	50000	5000000						3	0.310
2020-08-05T01:32:54	GAN	LMS-13	50000	5000000						3	0.310
2020-08-13T05:44:42	GAN	LMS-08	50000	5000000						3	0.310
2020-09-02T06:19:58	mnd9	kitchen	50000	5000000	3208200092868214522031	71.442	1	2	864573504979754	1	0.103

date	userid	compid	res64	spent (GHz-days)
1999-04-23T00:00:00	foxkid	v4_computers	1DBB4D952FE5D3C4	0.207
2018-07-26T09:52:26	kkmrkkblmbrbk	old	1DBB4D952FE5D3C4	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 = 2000000, B2 = 50000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 907827, B2 = 3631308 (P-1 stage 2)

B1 = 907827, B2 = 1815654 (P-1 stage 2)

B1 = 907827 (P-1 stage 1)

B1 = 314856, B2 = 3148560 (P-1 stage 2)

B1 = 151841, B2 = 4567500 (P-1 stage 2)

B1 = 377827 (P-1 stage 1)

B1 = 314856 (P-1 stage 1)

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

B1 = 218650 (P-1 stage 1)

B1 = 182209 (P-1 stage 1)

B1 = 151841 (P-1 stage 1)

B1 = 105000 (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

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