M2136733 Mersenne number exponent details

is 2 ^2136733 - 1

has 643221 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	27.8953	67.6471%	2500000	125000000	0.8746	7.9120%	28.7700	70.2068%	2.5598%
PrimeNet	2⁵⁸	0.0180	62.0690%	9000	170000	0.0017	2.7306%	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	+27.6078	+3.1309%	+2490000	+124850000	+0.8730	+6.4249%	+28.4808	+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
2136733	5787086245325020262026313	25	82.259	1354190309534466932 2² × 11 × 947 × 24623 × 1319884963	2020-03-17	24623	1319884963	908,058	6.8580	12.805

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%
2010-10-26T02:00:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.669%
2010-11-26T14:36:00	Oscar Östlin		80000	1500000		-		-	-	0.015	-	-	2.103%
2013-11-15T17:52:00	c10ck3r	Manual testing	500000	10000000		-		-	-	0.097	-	-	4.330%
2017-10-12T13:05:54	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	-	-
2009-01-04T23:52:00	Sturle Sunde	eberlin.ifi	2⁶⁰	2⁶¹		-	-	0.072	-	-
2012-04-15T18:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.144	-	-
2013-02-21T00:57:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.459	-	-
2015-03-18T10:56:00	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		-	-	3.497	-	-
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:	5.629 GHz-days
Estimated T-Level:	3.300

Digits	B1	Curves	Complete	FacMiss
20	11000	66 / 100	0.660	51.514%
25	50000	66 / 280	0.236	78.967%

New Calculation Method

Total ECM effort:	5.629 GHz-days
Estimated T-Level:	3.300

Digits	B1	Complete	FacMiss
20	11000	2.129	11.895%
25	50000	0.192	82.496%
30	250000	0.012	98.822%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		65	5.543
50000	5000000	5787086245325020262026313	1	0.085

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-12T22:12:00	TeamResslerTUB	1062323	50000	5000000						3	0.256
2009-11-21T22:32:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.256
2011-01-09T03:51:00	Oscar Östlin		50000	5000000						2	0.171
2012-11-26T07:22:00	Donna Noble	q8200v2	50000	5000000						3	0.256
2014-02-23T09:51:00	arnaud	srv-630	50000	5000000						3	0.256
2015-07-01T21:58:00	guru	w1	50000	5000000						3	0.256
2016-02-19T00:32:56	Jason U	Server7	50000	5000000						3	0.256
2016-05-03T22:37:31	Bruce	Desk6	50000	5000000						3	0.256
2016-08-10T15:59:25	Bruce	Desk6	50000	5000000						3	0.256
2016-12-29T08:54:07	Bruce	Desk6	50000	5000000						3	0.256
2017-07-22T01:40:25	Bruce	Desk6	50000	5000000						3	0.256
2017-12-21T07:43:29	Bruce	Desk6	50000	5000000						3	0.256
2018-05-19T07:11:24	Bruce	Desk6	50000	5000000						3	0.256
2019-01-14T22:30:41	Section 31	vengeance	50000	5000000						3	0.256
2020-01-18T19:06:02	EricP	Cannonfodder	50000	5000000						3	0.256
2020-01-24T08:50:27	daveward2005	Davy	50000	5000000						3	0.256
2020-02-01T12:42:01	daveward2005	Davy	50000	5000000						3	0.256
2020-02-11T05:03:03	cappy95833	HomePC	50000	5000000						3	0.256
2020-02-18T00:13:42	Nesowa	6700T	50000	5000000						3	0.256
2020-02-24T19:05:19	mnd9	office2	50000	5000000						3	0.256
2020-03-03T09:07:59	Alvin Bunk	BADCAT	50000	5000000						3	0.256
2020-03-08T22:37:44	Keysarecool	HPLaptop	50000	5000000						3	0.256
2020-03-17T04:47:25	mnd9	colab	50000	5000000	5787086245325020262026313	82.259	1	2	8737786273074459	1	0.085

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	ANONYMOUS	v4_computers	CC0EA4526BA282__	0.140
1999-06-06T00:00:00	ANONYMOUS	v4_computers	672C6C1657C87BD9	0.140
2018-04-06T23:51:14	kkmrkkblmbrbk	old	672C6C1657C87BD9	0.140

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-03-17T23:03:35

Niels_Mache_Nextcloud

SuperDry-X

5787086245325020262026313

F9845220A7A53CEE

2020-03-18T22:21:39

marssystems

system11

5787086245325020262026313

F9845220A7A53CEE

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

10¹⁰

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-03-18T22:21:39+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