M2136593 Mersenne number exponent details

is 2 ^2136593 - 1

has 643179 decimal digits

takes 0.140 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	2⁶⁸	27.8972	67.6471%	2500000	125000000	0.8746	7.9120%	28.7718	70.2068%	2.5598%
PrimeNet	2⁵⁸	0.0180	62.0690%	9000	170000	0.0017	2.7305%	0.0197	63.1047%	1.0357%
GPU72	2⁶²	0.2875	64.5161%	10000	150000	0.0017	1.4871%	0.2892	65.0438%	0.5277%
Difference	+6	+27.6096	+3.1309%	+2490000	+124850000	+0.8730	+6.4249%	+28.4826	+5.1630%	+5.1630%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2136593	55049260935506668413361	23	75.543	12882486494972760 2³ × 3 × 5 × 29 × 21991 × 168335407	2020-07-22	21991	168335407	6,604.7	0.8764	1.6331

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.224%
2010-10-26T04:34:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.669%
2010-11-26T14:18:00	Oscar Östlin		80000	1500000		-		-	-	0.015	-	-	2.103%
2013-11-15T17:52:00	c10ck3r	Manual testing	500000	10000000		-		-	-	0.097	-	-	4.330%
2017-10-12T08:50:40	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.912%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:06	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.054	-	-
2009-01-04T23:23:00	Sturle Sunde	eberlin.ifi	2⁶⁰	2⁶¹		-	-	0.072	-	-
2012-04-15T17:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.144	-	-
2013-02-21T00:57:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.459	-	-
2015-03-18T10:55:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.919	-	-
2015-03-18T10:56:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.749	-	-
2015-12-27T16:49:14	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.498	-	-
2016-10-29T15:24:09	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.995	-	-
2019-04-22T13:11:43	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.99	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.870 GHz-days
Estimated T-Level:	21.857

Digits	B1	Curves	Complete	FacMiss
20	11000	104 / 100	1.040	35.161%
25	50000	104 / 280	0.371	68.929%

New Calculation Method

Total ECM effort:	8.870 GHz-days
Estimated T-Level:	21.857

Digits	B1	Complete	FacMiss
20	11000	3.355	3.492%
25	50000	0.303	73.845%
30	250000	0.019	98.150%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		101	8.614
50000	5000000	55049260935506668413361	3	0.256

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-02T18:25:00	S36049	Wolle3	50000	5000000						3	0.256
2010-01-21T18:39:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.256
2011-01-08T23:58:00	Oscar Östlin		50000	5000000						2	0.171
2012-11-26T14:32:00	Donna Noble	CCI-i7-3770s-XP	50000	5000000						3	0.256
2014-02-23T06:09:00	arnaud	srv-630	50000	5000000						3	0.256
2015-07-01T20:39:00	guru	w6	50000	5000000						3	0.256
2016-02-19T05:13:53	Sintax	cloud	50000	5000000						3	0.256
2016-05-04T03:21:16	Jason U	Server7	50000	5000000						3	0.256
2016-08-10T13:10:13	Bruce	Desk6	50000	5000000						3	0.256
2016-12-29T07:57:08	Bruce	Desk6	50000	5000000						3	0.256
2017-07-21T19:07:51	Bruce	Desk6	50000	5000000						3	0.256
2017-12-21T05:12:42	Bruce	Desk6	50000	5000000						3	0.256
2018-05-19T05:01:52	Bruce	Desk6	50000	5000000						3	0.256
2019-01-11T06:53:04	Section 31	vengeance	50000	5000000						3	0.256
2020-01-19T08:01:32	David_McCann	i5	50000	5000000						3	0.256
2020-01-24T15:15:33	mnd9	25836b	50000	5000000						3	0.256
2020-02-01T16:31:58	J.R. Allen	lapdell	50000	5000000						3	0.256
2020-02-10T08:54:28	EricP	Cannonfodder	50000	5000000						3	0.256
2020-02-17T17:05:54	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.256
2020-02-24T18:27:07	mnd9	office2	50000	5000000						3	0.256
2020-03-02T14:28:59	MarkS	desktop-i7	50000	5000000						3	0.256
2020-03-02T15:41:59	MarkS	desktop-i7	50000	5000000						3	0.256
2020-03-16T11:18:16	mnd9	office2	50000	5000000						3	0.256
2020-03-26T13:24:36	daveward2005	MW	50000	5000000						3	0.256
2020-04-07T02:28:02	mnd9	221Rb	50000	5000000						3	0.256
2020-04-20T22:09:44	nordi	sweet16	50000	5000000						3	0.256
2020-04-28T12:36:20	nordi	sweet16	50000	5000000						3	0.256
2020-05-09T06:05:05	mnd9	50871b	50000	5000000						3	0.256
2020-05-22T07:31:05	Keysarecool	HPLaptop	50000	5000000						3	0.256
2020-06-10T12:57:18	mnd9	50871b	50000	5000000						3	0.256
2020-06-25T21:48:55	daveward2005	Davy	50000	5000000						3	0.256
2020-07-03T20:47:29	LaurV	3tits	50000	5000000						3	0.256
2020-07-10T10:02:08	GAN	GAN-HP	50000	5000000						3	0.256
2020-07-16T03:51:11	GAN	LMS-16	50000	5000000						3	0.256
2020-07-22T09:45:33	GAN	LMS-16	50000	5000000	55049260935506668413361	75.543	3	2	634477302076011	3	0.256

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	ANONYMOUS	v4_computers	BC1589FE361EDC25	0.140
2018-04-06T23:40:56	kkmrkkblmbrbk	old	BC1589FE361EDC25	0.140

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-07-23T02:58:52

argusdusty

Argus-PC

55049260935506668413361

86F04E9D15BFD731

2020-07-28T20:20:01

Yves Bellefeuille

Ryzen_1600

55049260935506668413361

86F04E9D15BFD731

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 = 2500000, B2 = 125000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 500000, B2 = 10000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 80000, B2 = 1500000 (P-1 stage 2)

B1 = 80000 (P-1 stage 1)

B1 = 75011 (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

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-07-28T20:20:01+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