M27134113 Mersenne number exponent details

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M27134113

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is 2 ^27134113 - 1

has 8168182 decimal digits

takes 25.118 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	0FBC8C5DEB29F717	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	2⁷¹	17.6191	64.7887%	305000	4041250	0.6826	3.4260%	18.3017	65.9951%	1.2063%
PrimeNet	2⁶⁶	0.5443	62.1212%	120000	4500000	0.4814	5.2122%	1.0257	64.0955%	1.9743%
GPU72	2⁷⁰	8.8063	64.2857%	200000	6000000	0.6926	3.9037%	9.4989	65.6799%	1.3942%
Difference	+1	+8.8128	+0.5030%	+105000	-1958750	-0.0100	-0.4777%	+8.8028	+0.3152%	+0.3152%

Known prime factors (1 factor, 67.3 bits, 0.00024816% known):

Remaining cofactor is PRP status unknown

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
27134113	186436475055587999423	21	67.337	3435462862847 281 × 12225846487	2011-11-15	281	12225846487	1.3924	894.07	1,669.9

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2005-02-12T00:00:00	amphoria	v4_computers	305000	4041250		-		-	-	0.683	-	-	3.426%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2011-11-15T00:11:00	Carsten Kossendey	Manual testing	?	?	186436475055587999423	67.337	21	0.297	51.20	0.606
2001-08-18T00:00:00	Net_Force	v4_computers	2¹	2⁵⁶		-	-	0.000	-	-
2002-08-31T00:00:00	Jocelyn Larouche	v4_computers	2¹	2⁵⁷		-	-	0.001	-	-
2004-03-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.023	-	-
2004-10-03T00:00:00	Philippe.Rose	v4_computers	2¹	2⁶⁷		-	-	1.095	-	-
2004-11-03T00:00:00	Philippe.Rose	v4_computers	2¹	2⁶⁷		-	-	1.095	-	-
2011-11-15T00:10:00	Carsten Kossendey	Manual testing	2⁶⁷	2⁷¹	MISSED FACTOR!	-	-	16.52	-	-

ECM factoring results:
No ECM results for M27134113

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2005-02-12T00:00:00	amphoria	v4_computers	0FBC8C5DEB29F717	25.12

PRP results:
No PRP results for M27134113

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 = 305000, B2 = 4041250 (P-1 stage 2)

B1 = 305000 (P-1 stage 1)

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TF factor-bounds graph:

2⁷¹

2⁶⁷

2⁶²

2⁵⁷

2⁵⁶

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2011-11-15T00:11:05+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