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Re: [PrimeNumbers] gen Cullen/Woodalls

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  • Pavlos S
    Indeed,the non-existence of a finite covering set does not prove infinite number of primes.Some time ago i had constructed a possible -infinite covering set
    Message 1 of 4 , Mar 8, 2004
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      Indeed,the non-existence of a finite covering set does
      not prove infinite number of primes.Some time ago i
      had constructed a "possible"-infinite covering set for
      the Sierpinski numbers which used the algebraic
      factoring of 4*X^4+1.

      --- Jens Kruse Andersen <jens.k.a@...> wrote:
      > Thomas wrote:
      >
      > > What do you think, does there exist a base b such
      > that n*b^n-1 or
      > > n*b^n+1 never is prime?
      > >
      > > I have no answer to that question, but maybe it is
      > easy for some of
      > > you to create such a base b, so that n*b^n +1/-1
      > always have small
      > > factors.
      >
      > No base b has a finite covering set of factors.
      > If M is a finite set then let A be the product of
      > the members.
      > If n=k*A for any k, then n*b^n+/-1 clearly never has
      > a factor in M.
      >
      > This does not necessarily mean there always is a
      > prime.
      > There could be an algebraic factor I have
      > overlooked. I know little about that.
      > If there is not then heuristics seem to support
      > infinitely many primes for all
      > b.
      >
      > --
      > Jens Kruse Andersen
      >
      >


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