M2441773 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	24.4105	67.6471%	1172000	48000000	0.3647	6.4333%	24.7752	69.7284%	2.0814%
PrimeNet	2⁵⁹	0.0315	62.7119%	10000	180000	0.0019	2.5267%	0.0333	63.6540%	0.9421%
GPU72	2⁶³	0.6536	65.0794%	10000	150000	0.0017	1.3067%	0.6554	65.5357%	0.4563%
Difference	+5	+23.7569	+2.5677%	+1162000	+47850000	+0.3630	+5.1266%	+24.1199	+4.1927%	+4.1927%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2441773	52337471444920152692479	23	75.470	10717104219950043 3² × 17 × 239 × 881 × 332668909	2020-11-29	881	332668909	5,374.2	1.7755	3.3160

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.233%
2003-10-31T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.771%
2010-11-17T22:12:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.262%
2011-01-12T12:43:00	Oscar Östlin		95000	1947500		-		-	-	0.019	-	-	2.372%
2014-01-19T13:34:00	mikr	MSI	1172000	48000000		-		-	-	0.365	-	-	6.433%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.031	-	-
2016-02-23T16:29:14	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.031	-	-
2009-01-15T00:09:00	Sturle Sunde	homilius.ifi	2⁶⁰	2⁶¹		-	-	0.063	-	-
2012-06-06T17:42:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.126	-	-
2013-12-04T21:13:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.402	-	-
2015-02-27T20:41:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.804	-	-
2015-02-27T20:41:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.530	-	-
2015-10-25T20:35:02	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.060	-	-
2017-07-12T11:35:13	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.121	-	-
2019-04-22T13:11:33	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.24	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.745 GHz-days
Estimated T-Level:	4.900

Digits	B1	Curves	Complete	FacMiss
20	11000	98 / 100	0.980	37.346%
25	50000	98 / 280	0.350	70.425%

New Calculation Method

Total ECM effort:	8.745 GHz-days
Estimated T-Level:	4.900

Digits	B1	Complete	FacMiss
20	11000	3.769	2.307%
25	50000	0.349	70.557%
30	250000	0.022	97.824%
35	1000000	0.001	99.897%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		93	8.299
50000	5000000	52337471444920152692479	5	0.446

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-06T14:55:00	Aca Arsov	backo6400	50000	5000000						3	0.268
2010-03-07T14:35:00	James Classen	towerofart	50000	5000000						3	0.268
2012-04-13T21:35:00	S36049	Wolle5	50000	5000000						3	0.268
2013-12-26T21:37:00	Andy Incline	Office-PC	50000	5000000						3	0.268
2015-07-07T02:41:00	guru	w6	50000	5000000						3	0.268
2016-04-24T05:18:23	Bruce	Desk6	50000	5000000						3	0.268
2016-06-15T06:41:57	Bruce	Desk6	50000	5000000						3	0.268
2016-10-22T20:03:47	Bruce	Desk6	50000	5000000						3	0.268
2017-04-27T03:24:47	Bruce	Desk6	50000	5000000						3	0.268
2017-11-26T06:55:53	Bruce	Desk6	50000	5000000						3	0.268
2018-05-12T16:11:33	Bruce	Desk6	50000	5000000						3	0.268
2019-06-02T14:43:59	Stefan G. Hoffmann	PC-HRW-2017-Dell	50000	5000000						3	0.268
2020-04-25T19:26:24	nordi	sweet16	50000	5000000						3	0.268
2020-05-04T01:34:02	Oliver Kruse	IOS-1	50000	5000000						3	0.268
2020-05-15T17:28:10	mnd9	27016b	50000	5000000						3	0.268
2020-06-01T12:40:49	GAN	PG	50000	5000000						3	0.268
2020-06-21T06:25:57	Summy	CHB	50000	5000000						3	0.268
2020-07-01T02:46:18	GAN	LMS-03	50000	5000000						3	0.268
2020-07-08T01:36:31	daveward2005	Davy	50000	5000000						3	0.268
2020-07-14T05:32:32	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.268
2020-07-20T06:43:15	daveward2005	Dave2	50000	5000000						3	0.268
2020-07-26T16:58:09	daveward2005	Davy	50000	5000000						3	0.268
2020-08-03T11:51:29	GAN	AC-GR	50000	5000000						3	0.268
2020-08-10T15:31:27	GAN	LMS-18	50000	5000000						3	0.268
2020-08-28T00:43:42	Nesowa	entropy_generator_2	50000	5000000						7	0.625
2020-09-28T16:01:20	mnd9	50871b	50000	5000000						7	0.625
2020-10-25T08:24:52	Keysarecool	Boat_Anchor	50000	5000000						7	0.625
2020-11-29T02:32:47	Zenzoma	i7-6820HQ	50000	5000000	52337471444920152692479	75.470	5	2	3426474438095633	5	0.446

date	userid	compid	res64	spent (GHz-days)
1999-09-14T00:00:00	ANONYMOUS	v4_computers	1685D61B10A55666	0.165
2018-05-24T10:54:54	kkmrkkblmbrbk	old	1685D61B10A55666	0.165

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 = 1172000, B2 = 48000000 (P-1 stage 2)

B1 = 1172000 (P-1 stage 1)

B1 = 95000, B2 = 1947500 (P-1 stage 2)

B1 = 95000 (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

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