M67271509 Mersenne number exponent details

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M67271509

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is 2 ^67271509 - 1

has 20250743 decimal digits

takes 170.047 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

-unknown- primality tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
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	2⁷⁴	56.8720	63.5135%	600000	10950000	4.2660	3.8311%	61.1380	64.9113%	1.3978%
PrimeNet	2⁷⁰	3.5520	61.4286%	280000	13000000	3.5664	5.3215%	7.1184	63.4812%	2.0526%
GPU72	2⁷⁴	56.8720	63.5135%	450000	15000000	4.5549	3.9304%	61.4269	64.9476%	1.4341%
Difference	-	-	-	+150000	-4050000	-0.2889	-0.0993%	-0.2889	-0.0362%	-0.0362%

Known prime factors (1 factor, 86.4 bits, 0.00012840% 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
67271509	100659762125508970490227337	27	86.380	748160429443532852 2² × 43 × 6761 × 205487 × 3130913	2013-09-30	205487	3130913	367,691	1.3374	1.5328

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2013-09-30T15:27:00	Jwb52z	Clay	600000	10950000			100659762125508970490227337	27	86.380	4.266	340.1	8.532	3.831%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-12-13T17:16:00	Wojciech Florek	Manual testing	2⁶³	2⁶⁴		-	-	0.029	-	-
2009-12-30T08:10:00	arnaud	ARNAUD	2⁶⁴	2⁶⁵		-	-	0.056	-	-
2009-12-31T02:42:00	arnaud	ARNAUD	2⁶⁵	2⁶⁶		-	-	0.111	-	-
2010-05-04T04:19:00	wavelet3000	elixir2	2⁶⁶	2⁶⁷		-	-	0.222	-	-
2010-05-06T06:20:00	unconnected	sau07	2⁶⁷	2⁶⁸		-	-	0.444	-	-
2010-05-09T01:02:00	unconnected	sau07	2⁶⁸	2⁶⁹		-	-	0.889	-	-
2012-05-22T16:17:00	sikafarmi_rendering_farm	Manual testing	2⁶⁹	2⁷⁰		-	-	1.777	-	-
2013-09-04T08:45:00	Axelsson	Manual testing	2⁷⁰	2⁷¹		-	-	3.555	-	-
2013-09-04T08:45:00	Axelsson	Manual testing	2⁷¹	2⁷²		-	-	7.109	-	-
2013-09-04T08:45:00	Axelsson	Manual testing	2⁷²	2⁷³		-	-	14.22	-	-
2013-09-04T17:01:00	Axelsson	Manual testing	2⁷³	2⁷⁴		-	-	28.44	-	-

ECM factoring results:
No ECM results for M67271509

Lucas-Lehmer results:
No L-L results for M67271509

PRP results:
No PRP results for M67271509

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 = 600000, B2 = 10950000 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁷⁴

2⁷³

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2013-09-30T15:27:42+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