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  • Bob Gilson
    Let a,b,c be consecutive natural numbers, where a  1 (a*c)-b appears to offer a greater density of primes than the norm; why? [Non-text portions of this
    Message 1 of 8 , Jun 5, 2008
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      Let a,b,c be consecutive natural numbers, where a >1
      (a*c)-b appears to offer a greater density of primes than the norm; why?

      [Non-text portions of this message have been removed]
    • Chris Caldwell
      From: Bob Gilson ... why? Call them n-1, n, and n+1 instead of a, b and c. Then a*c-b is n^2 - n - 1. This is never divisible by 2, so produces twice the
      Message 2 of 8 , Jun 5, 2008
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        From: Bob Gilson
        > Let a,b,c be consecutive natural numbers, where a >1
        > (a*c)-b appears to offer a greater density of primes than the norm;
        why?

        Call them n-1, n, and n+1 instead of a, b and c. Then a*c-b is
        n^2 - n - 1. This is never divisible by 2, so produces twice the
        primes "as usual." It is never divisible by 3, so that gives a
        factor of 3/2. Nor by 7, that gives 7/6. So with these alone
        we expect 3.5 times the usual number.

        CC
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