M2728247 Mersenne number exponent details

≡

M2728247

<<<

>>>

is 2 ^2728247 - 1

has 821285 decimal digits

takes 0.211 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	30CFD28F95CE7CA9	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	10.8912	67.1642%	2700000	84000000	0.7984	8.3225%	11.6897	69.8969%	2.7328%
PrimeNet	2⁵⁹	0.0281	62.7119%	12000	220000	0.0026	2.8484%	0.0308	63.7740%	1.0621%
GPU72	2⁶³	0.5850	65.0794%	14000	240000	0.0029	1.7064%	0.5879	65.6753%	0.5959%
Difference	+4	+10.3062	+2.0848%	+2686000	+83760000	+0.7955	+6.6161%	+11.1017	+4.2217%	+4.2217%

Known prime factors (1 factor, 99.2 bits, 0.00363613% 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
2728247	729333163639938787148672012407	30	99.202	133663331003376671384349 3 × 7 × 11 × 12421 × 59809 × 220333 × 3535067	2016-10-16	220333	3535067	6.941e+10	0.0449	0.0502

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.298%
2003-11-28T00:00:00	Team Prime Rib	v4_computers	15000	225000		-		-	-	0.003	-	-	0.932%
2010-12-19T21:42:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.320%
2010-12-28T02:16:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.439%
2011-01-19T23:50:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.628%
2011-04-25T16:05:00	James Heinrich	WHS	185000	4578750		-		-	-	0.048	-	-	3.684%
2016-10-16T17:58:02	mikr	MSI	2700000	84000000	12		729333163639938787148672012407	30	99.202	0.798	0.421	1.597	8.322%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-01-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.028	-	-
2016-02-23T16:29:20	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.028	-	-
2009-01-31T02:04:00	Sturle Sunde	goscha.ifi	2⁶⁰	2⁶¹		-	-	0.056	-	-
2012-04-15T13:09:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.113	-	-
2013-01-14T12:26:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.360	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.720	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.370	-	-
2016-02-01T09:40:54	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.739	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.867 GHz-days
Estimated T-Level:	0.900

Digits	B1	Curves	Complete	FacMiss
20	11000	18 / 100	0.180	83.451%
25	50000	18 / 280	0.064	93.763%

New Calculation Method

Total ECM effort:	1.867 GHz-days
Estimated T-Level:	0.900

Digits	B1	Complete	FacMiss
20	11000	0.581	55.954%
25	50000	0.052	94.888%
30	250000	0.003	99.677%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		18	1.867

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-15T07:05:00	Lukasz Wrobel	UNIX_05	50000	5000000						3	0.311
2010-08-25T12:54:00	James Classen	towerofart	50000	5000000						3	0.311
2013-03-08T18:33:00	Donna Noble	opt4820	50000	5000000						3	0.311
2015-02-28T10:35:00	S36049	Wolle5	50000	5000000						3	0.311
2016-02-07T20:39:02	Tapio Pätilä	JULIUS	50000	5000000						3	0.311
2016-05-05T21:12:57	lettp	Home	50000	5000000						3	0.311

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-01-13T00:00:00	ANONYMOUS	v4_computers	30CFD28F95CE7CA9	0.211
1999-04-13T00:00:00	S00030	v4_computers	30CFD28F95CE7CA9	0.211

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-20T01:48:02

Oliver Kruse

GTX-2

729333163639938787148672012407

6017177A3B72BA__

2017-12-05T06:25:59

kkmrkkblmbrbk

c4.xlarge

729333163639938787148672012407

6017177A3B72BA__

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 = 2700000, B2 = 84000000 (P-1 stage 2)

B1 = 2700000 (P-1 stage 1)

B1 = 185000, B2 = 4578750 (P-1 stage 2)

B1 = 185000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 225000 (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)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2017-12-05T06:25:59+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