M2684093 Mersenne number exponent details

≡

M2684093

<<<

>>>

is 2 ^2684093 - 1

has 807993 decimal digits

takes 0.207 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	605A2564932B49C9	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	11.0704	67.1642%	2000000	60000000	0.5779	7.7030%	11.6483	69.6935%	2.5293%
PrimeNet	2⁵⁹	0.0286	62.7119%	12000	220000	0.0026	2.8400%	0.0312	63.7708%	1.0590%
GPU72	2⁶³	0.5946	65.0794%	13000	220000	0.0027	1.6228%	0.5973	65.6461%	0.5667%
Difference	+4	+10.4758	+2.0848%	+1987000	+59780000	+0.5752	+6.0802%	+11.0509	+4.0475%	+4.0475%

Known prime factors (1 factor, 68.1 bits, 0.00253741% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2684093	317742032953366023689	21	68.106	59189833018708 2² × 7² × 301988943973	2017-11-15	49	301988943973	34.490	1,842.6	3,441.5

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.297%
2003-11-28T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.919%
2010-11-20T12:25:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.319%
2010-12-04T09:46:00	markr	tiny	105000	2283750		-		-	-	0.025	-	-	2.866%
2016-06-15T12:00:40	Jocelyn Larouche	Manual testing	161804	4567500	6	-		-	-	0.045	-	-	3.596%
2016-12-19T18:37:56	Jocelyn Larouche	low 4M	194164	194164		-		-	-	0.022	-	-	1.370%
2017-01-10T10:25:17	Jocelyn Larouche	low 4M	232996	232996		-		-	-	0.026	-	-	1.499%
2017-04-07T19:41:23	Jocelyn Larouche	low 4M	335514	3355140	6	-		-	-	0.056	-	-	3.714%
2019-07-04T12:48:34	alpertron	Manual testing	2000000	60000000	12	-		-	-	0.578	-	-	7.703%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:19	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.057	-	-
2009-01-31T00:48:00	Sturle Sunde	goober.ifi	2⁶⁰	2⁶¹		-	-	0.057	-	-
2012-05-11T12:38:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.114	-	-
2013-01-14T12:26:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.366	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.731	-	-
2015-02-23T17:25:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.392	-	-
2016-01-26T10:48:52	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.784	-	-
2017-09-13T08:55:33	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.568	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.691 GHz-days
Estimated T-Level:	1.300

Digits	B1	Curves	Complete	FacMiss
20	11000	26 / 100	0.260	77.004%
25	50000	26 / 280	0.093	91.117%

New Calculation Method

Total ECM effort:	2.691 GHz-days
Estimated T-Level:	1.300

Digits	B1	Complete	FacMiss
20	11000	0.839	43.227%
25	50000	0.076	92.700%
30	250000	0.005	99.534%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		24	2.484
50000	5000000	317742032953366023689	2	0.207

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-23T04:27:00	wuxiao	DNE_Black_Sheep	50000	5000000						3	0.310
2010-07-28T18:42:00	ANONYMOUS		50000	5000000						3	0.310
2012-12-30T19:26:00	Sara	Sara	50000	5000000						3	0.310
2014-12-28T07:37:00	arnaud	srv-630	50000	5000000						3	0.310
2016-02-01T11:39:10	arnaud	ATTAX14	50000	5000000						3	0.310
2016-04-19T09:19:33	AnthonyRais	Main	50000	5000000						3	0.310
2016-10-09T14:16:20	Ensigma	vps_sing	50000	5000000						3	0.310
2017-07-09T11:59:59	AnthonyRais	Win10Test	50000	5000000						3	0.310
2017-11-15T20:38:51	Chang Chia-Tche	ex-ctcpc	50000	5000000	317742032953366023689	68.106	2	2		2	0.207

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-04-13T00:00:00	foxkid	v4_computers	605A2564932B49C9	0.207

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-16T12:39:42

kkmrkkblmbrbk

c4.xlarge

317742032953366023689

9C4AE9101DD600__

2017-11-16T23:53:05

Oliver Kruse

GTX-3

317742032953366023689

9C4AE9101DD600__

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 = 2000000, B2 = 60000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 335514, B2 = 3355140 (P-1 stage 2)

B1 = 161804, B2 = 4567500 (P-1 stage 2)

B1 = 335514 (P-1 stage 1)

B1 = 232996 (P-1 stage 1)

B1 = 105000, B2 = 2283750 (P-1 stage 2)

B1 = 194164 (P-1 stage 1)

B1 = 161804 (P-1 stage 1)

B1 = 105000 (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

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2019-07-04T12:48:34+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