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Re: Prime 19-tuplet

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  • woodhodgson@xtra.co.nz
    ... Thank you for the extra clarification.
    Message 1 of 37 , Jun 3, 2011
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      --- In primenumbers@yahoogroups.com, "Jens Kruse Andersen" <jens.k.a@...> wrote:
      >
      > woodhodgson wrote:
      > > --- In primenumbers@yahoogroups.com, Tom Hadley <kctom99@> wrote:
      > >> The first 25 primes do not make an admissible constellation. It is
      > >> impossible to find that pattern repeated anywhere else.
      > >
      > > That's why I quoted 23, ignoring the "special" first century. There is no
      > > reason
      > > to rule out the existence of some 23-tuple "inside" a century somewhere.
      >
      > Right. However, the densest admissible 23-tuples have width 94 but
      > cannot be inside a century. They must start with a number which is
      > 7 or 9 (mod 10) and then they will cross a multiple of 100.
      > But there are admissible 23-tuples with width 96 which can be inside
      > a century, for example
      > {1,3,7,9,13,21,27,31,37,39,43,49,57,63,67,69,73,79,81,87,91,93,97}
      >
      > The densest admissible 24-tuples have width 100 so they obviously
      > don't fit inside a century.
      >
      > --
      > Jens Kruse Andersen
      >

      Thank you for the extra clarification.
    • Jens Kruse Andersen
      ... Congratulations! http://users.cybercity.dk/~dsl522332/math/simultprime.htm is updated. -- Jens Kruse Andersen
      Message 37 of 37 , Dec 31, 2012
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        Jaroslaw Wroblewski wrote:
        > Here is 5th known large prime 19-tuplet:
        >
        > 2406179998282157386567481191 + d,
        > d = 0, 6, 10, 16, 18, 22, 28, 30, 36, 42, 46, 48, 52, 58, 60, 66, 70, 72, 76
        > (28 digits, Dec 2012, Raanan Chermoni & Jaroslaw Wroblewski)
        >
        > This sets new records for 18 and 19 Simultaneous Primes.

        Congratulations!
        http://users.cybercity.dk/~dsl522332/math/simultprime.htm is updated.

        --
        Jens Kruse Andersen
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