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RE: [PrimeNumbers] Find the next prime

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  • Chris Caldwell
    If 2^n+1 is prime, n must be a power of 2 (2^0, 2^1, ...) and only the five are known. So for 2^((p-1)/2) + 1 to be prime, p must also be a Fermat prime. CC
    Message 1 of 69 , Sep 30, 2008
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      If 2^n+1 is prime, n must be a power of 2 (2^0, 2^1, ...) and only the five are known.

      So for 2^((p-1)/2) + 1 to be prime, p must also be a Fermat prime.

      CC

      -----Original Message-----
      From: primenumbers@yahoogroups.com [mailto:primenumbers@yahoogroups.com] On Behalf Of Sebastian Martin Ruiz
      Sent: Tuesday, September 30, 2008 11:41 AM
      To: primenumbers@yahoogroups.com
      Subject: [PrimeNumbers] Find the next prime



      Hello all:


      2^((pn-1)/2) + 1 is prime for n=2,3,7 (the primes are 3, 5, 257)

      Find the next. (Are all Fermat Primes?)

      Sincerely

      Sebastián Martin Ruiz





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    • 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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