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Re: consecutive twin primes

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  • Andrey Kulsha
    I think that such a chain exists. Heuristically there are infinite number of them. For example, numbers p+(0, 2, 12, 14, 30, 32, 42, 44, 72, 74, 78, 80, 108,
    Message 1 of 4 , May 31, 2001
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      I think that such a chain exists. Heuristically there are
      infinite number of them.

      For example, numbers

      p+(0, 2, 12, 14, 30, 32, 42, 44, 72, 74, 78, 80, 108, 110,
      120, 122, 150, 152)

      may be 18 consecutive primes infinitely many times
      (heuristically).

      Andrey
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    • Bouk de
      I am also confinced that such a chain is possible. It will be extremely rare though. You might want to check out: http://www.ltkz.demon.co.uk/ktuplets.htm A
      Message 2 of 4 , Jun 1, 2001
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        I am also confinced that such a chain is possible. It
        will be extremely rare though.

        You might want to check out:

        http://www.ltkz.demon.co.uk/ktuplets.htm

        A site which records record k-tuplet primes which is
        not unlike your search for consecutive twins.

        For example:

        2845372542509911868266807 + 0, 4, 10, 12, 16, 22, 24,
        30, 36, 40, 42, 46, 52, 54, 60, 64, 66, 70 (25 digits,
        2000, Joerg Waldvogel & Peter Leikauf)

        is the record 18-tuplet.

        You haven't made it easy for yourself with 9
        consecutive twins though;-)

        Have you found lesser chains already? Say 3 or 4
        consecutive twins?

        Bouk.


        --- Andrey Kulsha <Andrey_601@...> wrote:
        > I think that such a chain exists. Heuristically
        > there are
        > infinite number of them.
        >
        > For example, numbers
        >
        > p+(0, 2, 12, 14, 30, 32, 42, 44, 72, 74, 78, 80,
        > 108, 110,
        > 120, 122, 150, 152)
        >
        > may be 18 consecutive primes infinitely many times
        > (heuristically).
        >
        > Andrey
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      • Andrey Kulsha
        Hello! ... There are 7 chains of 8 consecutive twins below 10^13, found by Denis DeVries. This is a copy of his message sent on ... From: Denis DeVries
        Message 3 of 4 , Jun 1, 2001
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          Hello!

          Bouk de wrote:

          >Have you found lesser chains already? Say 3 or 4
          >consecutive twins?

          There are 7 chains of 8 consecutive twins below 10^13, found
          by Denis DeVries. This is a copy of his message sent on
          NMBRTHRY list:


          ----- Original Message -----
          From: Denis DeVries <ddevries2@...>
          To: <NMBRTHRY@...>
          Sent: Thursday, May 31, 2001 4:58 PM
          Subject: Twin Prime Groups


          > I've completed an exhaustive search of all primes through
          10^13 & found
          > seven sets of eight consecutive twin primes. There are no
          sets of nine
          > consecutive twins < 10^13.
          >
          > the seven "eight clusters" or "Octa-primes" are:
          >
          > 110 78197 32821 - 33063
          > 373 52832 49697 - 49963
          > 458 86461 46631 - 46813
          > 634 06985 79419 - 79619
          > 841 26497 48537 - 48689
          > 920 63598 43907 - 44179
          > 966 71456 61911 - 62129
          >
          > I'd be interested in hearing of the first discovery of a
          set of nine
          > consecutive twins.
          >
          > Denis DeVries
          > dhdevries@...
          ----------------------

          I guess that Jim Morton read this message and then asked our
          PrimeNumbers list about this problem (9 consecutive twins).

          Best wishes,

          Andrey
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