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22788Re: Primes >2

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  • paulunderwooduk
    Jul 7, 2011
      --- In primenumbers@yahoogroups.com, Dana Edgecomb <dedgecomb@...> wrote:
      >
      >
      > Prime numbers greater than two are those numbers, expressed in base two,
      > which contain a one in the rightmost position and and odd number of
      > ones, or (excluding leading zeroes) an odd number of zeroes, if there
      > are any.
      >
      >
      > Any base two number greater than two, with a zero in the rightmost
      > position is naturally a multiple of two, and hence not prime.
      >
      >
      > Any base two number with an even number of zeroes is naturally a
      > multiple of two smaller numbers, and hence not prime.
      >

      How about 2^43112609-1? It has zero -- an even number -- of 0's and an odd number of 1's, in base 2.

      7 = (111)_2 also fits,

      Paul
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