M2436311 Mersenne number exponent details

is 2 ^2436311 - 1

has 733403 decimal digits

takes 0.165 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁹	49.0031	68.1159%	1986400	69524000	0.5550	6.5902%	49.5581	70.2172%	2.1012%
PrimeNet	2⁵⁹	0.0315	62.7119%	10000	180000	0.0019	2.5256%	0.0334	63.6536%	0.9418%
GPU72	2⁶³	0.6551	65.0794%	10000	150000	0.0017	1.3061%	0.6568	65.5355%	0.4561%
Difference	+6	+48.3480	+3.0366%	+1976400	+69374000	+0.5533	+5.2841%	+48.9013	+4.6817%	+4.6817%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2436311	702706351054888946273	21	69.251	144215239978576 2⁴ × 13 × 693342499897	2022-01-08	16	693342499897	87.414	3,700.3	6,911.1

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	-	-	0.188%
2003-10-31T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.657%
2010-11-17T11:35:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.220%
2011-01-09T22:54:00	Oscar Östlin		95000	1923750		-		-	-	0.019	-	-	2.095%
2014-05-09T14:03:00	mikr	MSI	1986400	69524000		-		-	-	0.555	-	-	6.590%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-06-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.032	-	-
2016-02-23T16:29:14	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.032	-	-
2009-01-14T22:32:00	Sturle Sunde	gouache.ifi	2⁶⁰	2⁶¹		-	-	0.063	-	-
2012-06-05T21:42:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.126	-	-
2013-01-23T08:28:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.403	-	-
2015-02-27T20:40:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.806	-	-
2015-02-27T20:40:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.534	-	-
2015-10-25T20:35:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.067	-	-
2017-07-08T12:01:26	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.134	-	-
2019-06-03T11:26:15	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.27	-	-
2021-07-12T19:27:50	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	24.54	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	13.572 GHz-days
Estimated T-Level:	22.696

Digits	B1	Curves	Complete	FacMiss
20	11000	151 / 100	1.510	21.924%
25	50000	151 / 280	0.539	58.260%

New Calculation Method

Total ECM effort:	13.572 GHz-days
Estimated T-Level:	22.696

Digits	B1	Complete	FacMiss
20	11000	4.894	0.749%
25	50000	0.442	64.269%
30	250000	0.027	97.314%
35	1000000	0.001	99.875%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		135	12.04
50000	5000000	702706351054888946273	2	0.178
50000	5200000		7	0.635
50000	6750000		7	0.716

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-05T19:58:00	Aca Arsov	backo6400	50000	5000000						3	0.268
2010-03-05T00:36:00	James Classen	towerofart	50000	5000000						3	0.268
2012-04-04T02:30:00	S36049	Wolle5	50000	5000000						3	0.268
2013-12-21T22:53:00	arnaud	srv-630	50000	5000000						3	0.268
2015-07-05T16:05:00	guru	w1	50000	5000000						3	0.268
2016-02-21T01:58:39	Jason U	Server7	50000	5000000						3	0.268
2016-06-12T21:14:06	Bruce	Desk6	50000	5000000						3	0.268
2016-10-17T00:41:21	Bruce	Desk6	50000	5000000						3	0.268
2017-04-24T08:00:16	Bruce	Desk6	50000	5000000						3	0.268
2017-12-01T06:49:18	Sebastian Hornbostel	V2	50000	5000000						3	0.268
2018-05-06T11:54:42	Bruce	Desk6	50000	5000000						3	0.268
2019-05-23T04:02:29	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.268
2020-04-24T04:34:08	mnd9	75211backdoorb	50000	5000000						3	0.268
2020-05-01T10:34:36	nordi	sweet16	50000	5000000						3	0.268
2020-05-12T15:08:30	mnd9	eileen	50000	5000000						3	0.268
2020-05-28T21:54:53	mnd9	libproj	50000	5000000						3	0.268
2020-06-16T06:24:49	Summy	CHB	50000	5000000						3	0.268
2020-06-29T17:29:54	GAN	LMS-11	50000	5000000						3	0.268
2020-07-06T16:55:48	mnd9	office2	50000	5000000						3	0.268
2020-07-12T22:51:48	GAN	OSK-L2	50000	5000000						3	0.268
2020-07-18T19:16:30	GAN	OSB-02	50000	5000000						3	0.268
2020-07-24T23:58:33	GAN	LMS-06	50000	5000000						3	0.268
2020-08-01T17:47:29	GAN	KA-HP	50000	5000000						3	0.268
2020-08-08T20:53:23	GAN	LMS-18	50000	5000000						3	0.268
2020-08-18T17:18:21	Bommer	3900X	50000	5000000						7	0.624
2020-09-21T07:14:36	mnd9	50871b	50000	5000000						7	0.624
2020-10-21T00:22:36	mnd9	50869	50000	5000000						7	0.624
2020-11-22T20:22:54	Gerry Snyder	Gerry-Workstation	50000	5000000						7	0.624
2020-12-30T15:30:09	rextherunt	ice	50000	5000000						7	0.624
2021-01-29T09:02:48	Zenzoma	AMD3970X	50000	5000000						7	0.624
2021-02-27T19:42:29	RIHATEC	i7-3770K	50000	5000000						7	0.624
2021-04-03T05:23:27	Zenzoma	AMD3970X	50000	5000000						7	0.624
2021-05-20T16:33:55	kutens	canopus	50000	5200000						7	0.635
2021-07-17T07:51:27	lycorn	colab_S_2	50000	6750000						7	0.716
2021-08-26T15:15:41	RIHATEC	i7-3770K	50000	5000000						7	0.624
2022-01-08T16:17:22	MarkS	laptop64	50000	5000000	702706351054888946273	69.251	2	2	2954038572115746	2	0.178

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-26T00:00:00	ANONYMOUS	v4_computers	92EE702FD10C2B6F	0.165
2018-05-23T08:41:57	kkmrkkblmbrbk	old	92EE702FD10C2B6F	0.165

PRP results:

date

userid

compid

cofactors

res64

PRP

2022-01-09T08:33:13

LordJulius

WhiteBox

702706351054888946273

60E2461B5DBE58AD

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 = 1986400, B2 = 69524000 (P-1 stage 2)

B1 = 1986400 (P-1 stage 1)

B1 = 95000, B2 = 1923750 (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)

10⁰

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TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

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2⁶¹

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2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-01-09T08:33:13+00:00

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