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consecutive twin primes

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  • Jim Morton
    A number of us have been searching for nine consecutive twin primes. Consecutive meaning that there are no isolated single primes among the constellation . Is
    Message 1 of 4 , May 31 6:00 PM
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      A number of us have been searching for nine consecutive twin primes. Consecutive meaning that there are no isolated single primes among the "constellation".
      Is it possible (probable) that none exist?
      I don't think the Hardy-Littlewood conjecture covers this case.

      Jim Morton


      [Non-text portions of this message have been removed]
    • 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 2 of 4 , May 31 11:54 PM
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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 3 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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          > 220-86-71
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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 4 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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