M2686267 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	22.1887	67.6471%	2000000	50000000	0.5169	6.8677%	22.7056	69.8690%	2.2219%
PrimeNet	2⁵⁹	0.0286	62.7119%	12000	220000	0.0026	2.8404%	0.0312	63.7710%	1.0591%
GPU72	2⁶³	0.5941	65.0794%	13000	220000	0.0027	1.6230%	0.5969	65.6461%	0.5668%
Difference	+5	+21.5946	+2.5677%	+1987000	+49780000	+0.5141	+5.2447%	+22.1087	+4.2228%	+4.2228%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2686267	2922667207792622759738761	25	81.274	544001621542576140 2² × 3 × 5 × 17 × 64237 × 8302612561	2020-08-06	64237	8302612561	243,869	50.666	94.618

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%
2011-02-02T12:35:00	markr	tiny	105000	2283750		-		-	-	0.025	-	-	2.550%
2016-06-17T04:08:31	Jocelyn Larouche	Manual testing	167500	4567500	6	-		-	-	0.046	-	-	3.242%
2016-12-21T00:33:40	Jocelyn Larouche	low 4M	201000	201000		-		-	-	0.023	-	-	1.224%
2017-04-13T02:13:58	Jocelyn Larouche	low 4M	335000	3350000	6	-		-	-	0.056	-	-	3.342%
2018-07-09T21:12:19	Jocelyn Larouche	low 4M	670000	6700000	6	-		-	-	0.112	-	-	4.223%
2019-11-17T15:45:16	masser	Manual testing	2000000	50000000	12	-		-	-	0.517	-	-	6.868%

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	-	-
2009-02-01T02:39:00	Sturle Sunde	gerle.ifi	2⁶⁰	2⁶¹		-	-	0.057	-	-
2012-05-07T23:13:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.114	-	-
2013-01-14T12:26:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.365	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.731	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.391	-	-
2016-01-26T10:48:53	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.782	-	-
2017-09-13T08:55:34	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.564	-	-
2019-04-29T13:20:16	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.13	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.347 GHz-days
Estimated T-Level:	2.100

Digits	B1	Curves	Complete	FacMiss
20	11000	42 / 100	0.420	65.566%
25	50000	42 / 280	0.150	86.048%

New Calculation Method

Total ECM effort:	4.347 GHz-days
Estimated T-Level:	2.100

Digits	B1	Complete	FacMiss
20	11000	1.355	25.799%
25	50000	0.122	88.475%
30	250000	0.008	99.249%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		39	4.036
50000	5000000	2922667207792622759738761	3	0.310

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-06T21:05:00	Jürgen Decker	Q9550_home	50000	5000000						3	0.310
2010-08-02T05:05:00	Kamil_Górski	thefault	50000	5000000						3	0.310
2012-12-20T23:21:00	sannerud.com	Jens2010	50000	5000000						3	0.310
2015-01-01T02:47:00	arnaud	srv-630	50000	5000000						3	0.310
2016-01-30T17:32:38	Jason U	Server7	50000	5000000						3	0.310
2016-04-27T13:29:52	Palantsevich	OfficeB01	50000	5000000						3	0.310
2016-10-18T18:40:15	Marius Zens	KBWR_TV3	50000	5000000						3	0.310
2017-07-10T06:28:59	AnthonyRais	Win10Test	50000	5000000						3	0.310
2017-11-17T16:12:21	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.310
2018-06-15T14:27:12	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.310
2019-09-01T02:45:53	prime235711	prime235711	50000	5000000						3	0.310
2020-07-23T10:37:25	Ahmed Azhad	c5.4xlarge.azf	50000	5000000						3	0.310
2020-07-30T07:42:48	GAN	LMS-16	50000	5000000						3	0.310
2020-08-06T20:08:18	GAN	LMS-17	50000	5000000	2922667207792622759738761	81.274	3	2	8188189779661197	3	0.310

date	userid	compid	res64	spent (GHz-days)
1999-04-23T00:00:00	ANONYMOUS	v4_computers	523B7E5E72931BC0	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 = 670000, B2 = 6700000 (P-1 stage 2)

B1 = 670000 (P-1 stage 1)

B1 = 335000, B2 = 3350000 (P-1 stage 2)

B1 = 167500, B2 = 4567500 (P-1 stage 2)

B1 = 335000 (P-1 stage 1)

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

B1 = 201000 (P-1 stage 1)

B1 = 167500 (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