M2627869 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	2⁶⁹	45.4310	68.1159%	8000000	250000000	2.3725	8.9789%	47.8036	70.9788%	2.8628%
PrimeNet	2⁵⁹	0.0292	62.7119%	11000	200000	0.0024	2.7002%	0.0316	63.7187%	1.0068%
GPU72	2⁶³	0.6073	65.0794%	13000	200000	0.0026	1.5722%	0.6099	65.6284%	0.5490%
Difference	+6	+44.8237	+3.0366%	+7987000	+249800000	+2.3699	+7.4068%	+47.1936	+5.3504%	+5.3504%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-31T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.192%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.668%
2010-12-21T22:27:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.224%
2010-12-26T02:29:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.312%
2011-01-20T22:46:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.457%
2011-02-28T05:29:00	James Heinrich	i7-920	300000	8000000		-		-	-	0.081	-	-	3.584%
2018-07-20T10:11:40	mikr	S069	8000000	250000000	12	-		-	-	2.373	-	-	8.979%
2019-10-21T15:48:25	masser	Manual testing	2630000	26300000	12	-		-	-	0.439	-	-	5.704%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.029	-	-
2016-02-23T16:29:18	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.029	-	-
2009-01-29T03:08:00	Sturle Sunde	celair.ifi	2⁶⁰	2⁶¹		-	-	0.058	-	-
2012-06-16T18:14:00	Grant McCracken	home	2⁶¹	2⁶²		-	-	0.117	-	-
2013-01-14T11:57:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.374	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.747	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.422	-	-
2016-01-18T09:58:45	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.844	-	-
2017-09-01T23:24:07	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.687	-	-
2019-04-01T13:34:42	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.37	-	-
2021-06-14T11:23:25	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	22.75	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.754 GHz-days
Estimated T-Level:	22.536

Digits	B1	Curves	Complete	FacMiss
20	11000	142 / 100	1.420	23.999%
25	50000	142 / 280	0.507	60.167%

New Calculation Method

Total ECM effort:	14.754 GHz-days
Estimated T-Level:	22.536

Digits	B1	Complete	FacMiss
20	11000	5.484	0.415%
25	50000	0.507	60.209%
30	250000	0.032	96.849%
35	1000000	0.001	99.850%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		135	13.92
50000	6750000		7	0.830

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-02T18:43:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.309
2010-06-20T09:10:00	Lackó	Iroda_Laci	50000	5000000						3	0.309
2012-11-24T07:10:00	Donna Noble	PH2x6	50000	5000000						3	0.309
2014-10-03T18:13:00	arnaud	srv-630	50000	5000000						3	0.309
2015-12-14T19:39:18	guru	w1	50000	5000000						3	0.309
2016-04-02T05:09:02	lettp	Home	50000	5000000						3	0.309
2016-08-31T20:56:45	Marius Zens	KBWR_TV3	50000	5000000						3	0.309
2017-06-29T21:04:27	Ensigma	vps_sing	50000	5000000						3	0.309
2017-10-28T07:08:13	Sebastian Hornbostel	V2	50000	5000000						3	0.309
2018-04-27T10:52:10	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.309
2019-03-10T05:24:04	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.309
2020-07-10T04:15:49	GAN	LMS-15	50000	5000000						3	0.309
2020-07-16T08:35:52	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.309
2020-07-22T07:25:44	Ahmed Azhad	c5.4xlarge.azf	50000	5000000						3	0.309
2020-07-29T00:32:47	daveward2005	Dave2	50000	5000000						3	0.309
2020-08-05T21:58:53	mnd9	25836b	50000	5000000						3	0.309
2020-08-13T12:04:06	GAN	LMS-15	50000	5000000						3	0.309
2020-09-04T04:46:34	rextherunt	ice	50000	5000000						7	0.722
2020-10-06T12:02:26	MarkS	desktop-i7	50000	5000000						7	0.722
2020-11-02T21:58:13	mnd9	kitchen	50000	5000000						7	0.722
2020-12-09T10:25:34	Massimo Cappelli (ik5pwa)	maxwinxp_1	50000	5000000						7	0.722
2021-01-10T16:37:46	lycorn	colab_D_1	50000	5000000						7	0.722
2021-02-08T18:10:38	lycorn	colab_S_2	50000	6750000						7	0.830
2021-03-15T02:50:34	Zenzoma	AMD3970X	50000	5000000						7	0.722
2021-04-22T07:26:29	debrouxl		50000	5000000						7	0.722
2021-06-12T16:25:41	kutens	vega	50000	5000000						7	0.722
2021-07-24T13:39:12	MarkS	desktop-i7	50000	5000000						7	0.722
2021-11-17T20:40:11	RIHATEC	i7-3770K	50000	5000000						7	0.722
2021-12-12T02:37:38	daveward2005	d12436	50000	5000000						7	0.722
2022-04-03T11:15:48	daveward2005	d12436	50000	5000000						7	0.722

date	userid	compid	res64	spent (GHz-days)
1999-04-13T00:00:00	ANONYMOUS	v4_computers	9E22B5A13D812670	0.203

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 = 8000000, B2 = 250000000 (P-1 stage 2)

B1 = 8000000 (P-1 stage 1)

B1 = 2630000, B2 = 26300000 (P-1 stage 2)

B1 = 2630000 (P-1 stage 1)

B1 = 300000, B2 = 8000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 50000 (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

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