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Question about filters (sieve of Eratosthenes)

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  • gulland68
    The following is interpretable as a question about filters, indexed by the set of primes in the interval I define as [1,y], in the sieve of Eratosthenes, and
    Message 1 of 1 , Nov 21, 2008
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      The following is interpretable as a question about filters, indexed by
      the set of primes in the interval I define as [1,y], in the sieve of
      Eratosthenes, and how they can be arranged.

      Let x and y be integers such that 0<x<y.

      Let G(x,y) be the number of composites in an interval of length
      (y-x+1) that contain no factor in [2,y].

      If p is a prime in the set of primes in [1,y], is there a standard
      proof (or disproof) that, for all intervals [1+k,y+k] for which, for
      all p, there are floor(n/p) integers i for which p|i, G(1+k,y+k) plus
      the number of primes in [1,y] /\ [1+k,y+k] is maximal if k=0

      With thanks in advance.
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