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Re: [PrimeNumbers] distribution of primes mod 30.

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  • Phil Carmody
    ... Not just clear - proved. Dirichlet. ... or mod 30: 1, 7, 11, 13, 17, 19 23, 29 Also true by Dirichlet. Phil () ASCII ribbon campaign () Hopeless
    Message 1 of 2 , May 30, 2006
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      --- Kermit Rose <kermit@...> wrote:
      > A while back someone raised the question of the distribution of primes of
      > the form 2^p -1 , mod 10.
      >
      >
      > It's clear that for primes in general,
      >
      > prob( mod(prime,10) == 1) = 1/4
      > prob( mod(prime,10) == 3) = 1/4
      > prob( mod(prime,10) == 7) = 1/4
      > prob( mod(prime,10) == 9) = 1/4

      Not just clear - proved. Dirichlet.

      > I also observed that
      >
      > prob( mod( int(prime/10),3 ) == 0 ) = 1/4
      > prob( mod( int(prime/10),3 ) == 1 ) = 1/2
      > prob( mod( int(prime/10),3 ) == 2 ) = 1/4

      or mod 30:

      1, 7,
      11, 13, 17, 19
      23, 29

      Also true by Dirichlet.

      Phil

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