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Re: Identifying Prime Numbers

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  • jim_fougeron
    Hello Frank, Close but not quite right. What you have laid out, is that all number 7 are prime if they are not divisible by 2 (the odd part) or 3 or 7. This
    Message 1 of 2 , Aug 3, 2004
      Hello Frank,

      Close but not quite right.

      What you have laid out, is that all number > 7 are prime if they
      are not divisible by 2 (the odd part) or 3 or 7. This does not hold.

      The first failure is 25, and there are infinitely more failures.

      However, if you state that:

      "All primes larger than 7 are contained within the group of numbers
      that are not divisible by 2, 3, 5 or 7" then you have a true
      statement. However, that group of numbers is in no "pure" primes.
      It simply has had the composites with small factors (2, 3, 5, 7)
      removed.

      One additional item you might want to note, is that all numbers
      over 7 and under 7^2 (49) ARE prime, if they are not divisible by
      2, 3, 5, 7. This is one of the more trivial ways to prove primality.
      Simply test all primes up to number^(1/2) and if none of those
      primes evenly divide your candidate number, then it is proven to
      be prime. This method of proof, however, becomes computationally
      very time consuming, as the size of the number increases. Thus,
      this "trial factor proving" method is only used for the smallest
      of numbers.

      Jim.

      --- In primenumbers@yahoogroups.com, fcw44@a... wrote:
      > Hello All,
      >
      > I am new to this group, but have some ideas that I'd like to have
      aired.
      >
      > Giving some thought to primes recently, I developed a rather simple
      approach
      > to distinguish prime versus non-prime:
      >
      > For all odd numbers n>=7, primes will be the only numbers not
      evenly
      > divisible by either 3 or 7.
      >
      > I have done only limited testing on this hypothesis, because of
      resource
      > limitations. Appears to work through first 1000 primes.
      >
      > Frank Walsh
      >
      >
      > [Non-text portions of this message have been removed]
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