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Re: The house that Jack built

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  • Mike Oakes
    ... Pure chance. I have some experimental evidence for this, which shall be posted tomorrow. Mike
    Message 1 of 69 , Mar 25, 2009
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      --- In primenumbers@yahoogroups.com, "David Broadhurst" <d.broadhurst@...> wrote:
      >
      > Let x = sqrt(3) + sqrt(2).
      >
      > Then (x^n + 1/x^n)/(2*sqrt(3)) is prime (or PRP) for
      >
      > n = 5, 7, 13, 107, 227, 491, 8009, 36779 ...
      >
      > while (x^n - 1/x^n)/(2*sqrt(2)) is prime (or PRP) for
      >
      > n = 3, 5, 37, 41, 43, 59, 71, 113, 181, 293, 383, 421,
      > 1109, 1187, 1997, 3109, 4889, 5581 ...
      >
      > Puzzle: Why is the second Lehmer series more fertile at small n?

      Pure chance.
      I have some experimental evidence for this, which shall be posted tomorrow.
      Mike
    • 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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