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Re: A base 2 pseudo prime divides at most one prime-exponent Mersenne

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  • Kevin Acres
    Hi David, The only number that can divide a Mersenne is a base 2 pseudoprime or a prime. Now all composite Mersennes are, in fact, base 2 pseudoprimes. This
    Message 1 of 2 , Jun 29, 2004
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      Hi David,

      The only number that can divide a Mersenne is a base 2 pseudoprime or a prime.

      Now all composite Mersennes are, in fact, base 2 pseudoprimes.

      This means that at the simplest level, you only need know what the
      differences are between a pseudoprime and a prime.

      What I was getting at was that I have a method that differentiates a prime
      from a pseudoprime. Only that this method doesn't work (well) for Mersennes.

      But in order to understand why the method works you also need to understand
      what it is about a base 2 pseudoprime that lets it divide a Mersenne.

      Hence my earlier post.

      Regards,

      Kevin.



      At 12:22 PM 30/06/2004, David Broadhurst wrote:
      > > A prime number divides at most one prime-exponent Mersenne.
      >
      >A moment of reflection should tell you that this implies
      >that _every_ number > 1 divides at most prime exponent Mersenne.
      >[I omit the half-line proof.]
      >
      >So why single out this irrelevant special case:
      >
      > > A base 2 pseudo prime number divides at most one prime-exponent
      > > Mersenne.
      >
      >when it is a trivial consequnce of the statement
      >about prime divisors?
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