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RE: primes between squares calcs

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  • Bill
    OOPs! I left out a in my definition of Legendre s conjecture. Legendre s conjecture is of course for n=2 and m = 1. My apologies Bill
    Message 1 of 5 , Dec 9, 2010
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      OOPs! I left out a ">" in my definition of Legendre's conjecture.
      Legendre's conjecture is of course for n=2 and m >= 1.
      My apologies Bill
    • Aldrich
      ... Intuitively Legendre s conjecture would appear to be true: the rate of growth of the gap between squares looks like it would far exceed the rate of growth
      Message 2 of 5 , Dec 12, 2010
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        --- In primenumbers@yahoogroups.com, "Bill" <bill2math@...> wrote:
        >

        > Legendre's conjecture claims there is at least one prime between the squares of consecutive integers, and is Capelle's case with n=2 and m = 1.
        >

        Intuitively Legendre's conjecture would appear to be true: the
        rate of growth of the gap between squares looks like it would
        far exceed the rate of growth in the average gap between primes.
        However the pattern of these gaps can be very uneven and I believe that
        it HAS been proven that the gap between primes can be arbitrarily
        large. This does not disprove Legendre's conjecture - probably
        the only way to do that would be to find a counterexample. Good
        with that project!

        a.
      • Paul Leyland
        ... The proof is trivial. For prime p, all integers n s.t. p!+1
        Message 3 of 5 , Dec 12, 2010
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          On Sun, 2010-12-12 at 10:13 +0000, Aldrich wrote:
          > However the pattern of these gaps can be very uneven and I believe
          > that
          > it HAS been proven that the gap between primes can be arbitrarily
          > large. This does not disprove Legendre's conjecture - probably

          The proof is trivial. For prime p, all integers n s.t.
          p!+1 < n <= p!+p are divisible by at least one prime <= p and p can be
          taken arbitrarily large.

          Paul
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