## Re: [PrimeNumbers] Re: Mersenne Long Shot

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• This number is known as C5, after Catalan. It s mentioned in Dickson s History of Numbers. http://mathworld.wolfram.com/Catalan-MersenneNumber.html
Message 1 of 5 , Jan 23, 2006
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This number is known as C5, after Catalan. It's mentioned in Dickson's History
of Numbers.

http://mathworld.wolfram.com/Catalan-MersenneNumber.html

Noll/Caldwell have tested it against possible divisors
up to 10^51. At the moment, the only hope for deciding
Catalan's conjecture if finding a divisor.

Ed Pegg Jr

--- grostoon <grostoon@...> wrote:

> --- In primenumbers@yahoogroups.com, "Jon Perry" <perry@g...> wrote:
> >
> > Probably not the first to spot this, but
> >
> > 2^2-1=3
> > 2^3-1=7
> > 2^7-1=127
> > 2^127-1=170141183460469231731687303715884105727
> >
> > hence 2^170141183460469231731687303715884105727-1 stands a high
> probability
> > of being prime.
> >
> > Jon Perry
> > perry@g...
> > http://www.users.globalnet.co.uk/~perry/maths/
> > BrainBench MVP for HTML and JavaScript
> > http://www.brainbench.com
> >
>
> Hi Jon,
>
> Compute gcd(n^17 + 9, (n+1)^17 + 9) for n = 1, 2, 3, 4, ...
> You will found that it's always 1. You can try for all n < 10^3,
> 10^4, ... 10^20, ... 10^50, it's always 1.
>
> So can we conclude with a "high probability" that the gcd is actually
> always 1 ?
>
> Then, let's try n=8424432925592889329288197322308900672459420460792433
>
> J-L
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> The Prime Pages : http://www.primepages.org/
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