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Re: [PrimeNumbers] Re: Mersenne Long Shot

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  • ed pegg
    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/
      > > http://www.users.globalnet.co.uk/~perry/DIVMenu/
      > > 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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