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Re: binary prime number solution.

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  • Paul E. Schippnick
    Actually, Type n 2^(n-1)-1 mod n ... composite 1 = 0 prime 2 = 1 composite 341 = 1 composite 561 = 1 composite 645 = 1
    Message 1 of 5 , May 23, 2007
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      Actually,

      Type n 2^(n-1)-1 mod n
      --------- ---- -
      composite 1 => 0
      prime 2 => 1
      composite 341 => 1
      composite 561 => 1
      composite 645 => 1
      composite 1105 => 1
      composite 1387 => 1
      composite 1729 => 1
      composite 1905 => 1
      prime 1093 => 1, fails

      Thanks for your help.




      --- In primenumbers@yahoogroups.com, Alan McFarlane
      <alan.mcfarlane@...> wrote:
      >
      > Given a few test values, your function returns:
      >
      > Type n 2^(n-1)-1 mod n
      > --------- ---- -
      > composite 1 => 0
      > prime 2 => 1
      > composite 341 => 0
      > composite 561 => 0
      > composite 645 => 0
      > composite 1105 => 0
      > composite 1387 => 0
      > composite 1729 => 0
      > composite 1905 => 0
      >
      > Look at
      >
      > http://www.research.att.com/~njas/sequences/A001567
      >
      > Extract:
      >
      > "It is known that all primes p divide 2^(p-1) - 1"
      >
      >
      >
      > Paul E. Schippnick wrote:
      > >
      > >
      > > I recently discovered a prime number solution for all prime
      numbers. It
      > > works. And one of its proofs is where it fails. Yes, where it
      fails is a
      > > proof that it will work for all other prime numbers.
      > >
      > > Where it fails: Testing Mersenne Primes. Because of how it proves
      a
      > > prime, all Mersenne numbers test as if prime. And only the
      Mersenne
      > > composite numbers. That means non-Mersenne composite numbers will
      never
      > > test as prime.
      > >
      > > Here is the test formula: 2n-1 - 1 mod n = 0, then n is prime.
      > >
      > > Now it has other issues. But it is a binary test for prime.
      > > ----------
      > >
      > > No virus found in this outgoing message.
      > > Checked by AVG Free Edition.
      > > Version: 7.5.467 / Virus Database: 269.7.6/815 - Release Date:
      5/22/07
      > > 3:49 PM
      > >
      > > [Non-text portions of this message have been removed]
      > >
      > >
      >
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