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Re: The house that Jack built

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  • Jan van Delden
    If I understand the proposition correctly: if A(n),B(n) are prime then either n is prime (odd) or n is a power of 3. Maybe not very helpfull, because it can t
    Message 1 of 69 , Mar 24, 2009
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      If I understand the proposition correctly: if A(n),B(n) are prime then either n is prime (odd) or n is a power of 3.
      Maybe not very helpfull, because it can't provide a counterexample, but I found that for J(n): J(3n)=(J(n)-sqrt(3)) J(n) (J(n)+sqrt(3)), and J(1)=2*sqrt(3) gives for C(n)=J(n)/sqrt(3):
      C(3n)=3 (C(n)-1) C(n) (C(n)+1), C(1)=2. I tested the first powers of 3 untill 3^10 and didn't find any other prime values for C(n)+/-1=A(n) resp. B(n).
      [I used J(n)J(k)=J(k+n)+J(k-n), with k=2n and k=n and J(0)=2].

      Jan van Delden

      [Non-text portions of this message have been removed]
    • Mike Oakes
      ... Congrats! That size of 15537 digits is nearly 25% bigger than the next 12 on that Top-20 Lehmer Primitive Part list, which all date from more than 3
      Message 69 of 69 , May 10, 2009
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        --- In primenumbers@yahoogroups.com, "David Broadhurst" <d.broadhurst@...> wrote:
        >
        > --- In primenumbers@yahoogroups.com,
        > "David Broadhurst" <d.broadhurst@> wrote:
        >
        > > The Society for Suppression of Square Roots hopes to
        > > be able to announce, within a few days, the proof of
        > > a unique Lehmer prime with more than 15000 digits
        > > (wenn die Frau Göttin probiert hat).
        > > If proven, it will also become the largest known prime at
        > > http://primes.utm.edu/top20/page.php?id=68
        >
        > Consummatus est in brevi explevit tempora multa [Wisdom:4:13]
        >
        > http://primes.utm.edu/primes/page.php?id=88162#comments

        Congrats! That size of 15537 digits is nearly 25% bigger than the next 12 on that "Top-20" Lehmer Primitive Part list, which all date from more than 3 years ago. So, a massive improvement!

        Mike
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