M2566411 Mersenne number exponent details

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M2566411

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is 2 ^2566411 - 1

has 772567 decimal digits

takes 0.178 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	E6E7B60081B51ACB	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	11.5780	67.1642%	3200000	112000000	0.9180	8.7492%	12.4960	70.0371%	2.8729%
PrimeNet	2⁵⁹	0.0299	62.7119%	11000	200000	0.0021	2.6884%	0.0321	63.7143%	1.0025%
GPU72	2⁶³	0.6219	65.0794%	12000	180000	0.0021	1.4799%	0.6240	65.5962%	0.5168%
Difference	+4	+10.9561	+2.0848%	+3188000	+111820000	+0.9159	+7.2693%	+11.8720	+4.4409%	+4.4409%

Known prime factors (1 factor, 93.7 bits, 0.00365088% 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
2566411	16050439278904870791685067833	29	93.697	3127020434159780095956 2² × 3² × 17 × 23 × 137 × 149 × 2314097 × 4702871	2016-05-21	2314097	4702871	1.488e+9	0.2458	0.4737

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-23T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.293%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	198750		-		-	-	0.003	-	-	0.885%
2010-12-21T01:09:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.316%
2011-01-03T22:20:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.433%
2011-01-10T23:57:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.621%
2011-04-14T16:37:00	James Heinrich	WHS	175000	4112500		-		-	-	0.039	-	-	3.540%
2016-05-21T19:57:30	mikr	MSI	3200000	112000000	12		16050439278904870791685067833	29	93.697	0.918	0.356	1.836	8.749%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
2016-02-23T16:29:16	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.030	-	-
2009-01-29T19:55:00	Sturle Sunde	gilia.ifi	2⁶⁰	2⁶¹		-	-	0.060	-	-
2012-06-17T14:42:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.120	-	-
2013-01-23T08:30:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.383	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.765	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.456	-	-
2015-11-08T21:03:02	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.912	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.661 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:	1.661 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	1.661

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-16T17:42:00	Smurgs	Praca	50000	5000000						3	0.277
2010-05-24T06:13:00	Conductor	home	50000	5000000						3	0.277
2012-10-20T02:44:00	Syntony	Geomancer	50000	5000000						3	0.277
2014-04-22T22:32:00	Andy Incline	Office-PC	50000	5000000						3	0.277
2015-08-14T02:53:00	guru	w6	50000	5000000						3	0.277
2016-03-12T10:42:17	Jason U	Server7	50000	5000000						3	0.277

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-30T00:00:00	ANONYMOUS	v4_computers	B5C85FD3C18FAC__	0.178
1999-09-14T00:00:00	ANONYMOUS	v4_computers	E6E7B60081B51ACB	0.178

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-15T03:41:06

Oliver Kruse

GTX-2

16050439278904870791685067833

00EEFCF137D3BD__

2017-12-02T21:30:49

trebor

Laptop

16050439278904870791685067833

00EEFCF137D3BD__

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 = 3200000, B2 = 112000000 (P-1 stage 2)

B1 = 3200000 (P-1 stage 1)

B1 = 175000, B2 = 4112500 (P-1 stage 2)

B1 = 175000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 198750 (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

10⁹

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2017-12-02T21:30:49+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