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BiTwin

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  • jarek372000
    Yesterday I started a search aimed at 18 Simultaneous Primes (BiTwin). So far I failed to improve SP18 record, but I have determined that the number
    Message 1 of 4 , Dec 3, 2008
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      Yesterday I started a search aimed at 18 Simultaneous Primes (BiTwin).
      So far I failed to improve SP18 record, but I have determined that the
      number
      112511682470782472978100 = 1.12512*10^23
      is the only number N below 1.23056*10^23 which produces 18 primes by
      the formula
      N * 2^n +/- 1, n=0,...,8

      Jarek
    • Jens Kruse Andersen
      ... Congratulations on another great result! The first BiTwin with 8 links as defined at http://www.primenumbers.net/Henri/fr-us/BiTwinRec.htm It also beats
      Message 2 of 4 , Dec 3, 2008
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        Jarek wrote:
        > 112511682470782472978100 = 1.12512*10^23
        > is the only number N below 1.23056*10^23 which produces 18 primes by
        > the formula
        > N * 2^n +/- 1, n=0,...,8

        Congratulations on another great result!
        The first BiTwin with 8 links as defined at
        http://www.primenumbers.net/Henri/fr-us/BiTwinRec.htm
        It also beats the largest known with 7 links by Hans Rosenthal and I.

        --
        Jens Kruse Andersen
      • Jaroslaw Wroblewski
        ... Thanks. Another LUCKY result, I would say :-) At the moment I have the following solution count: 5 links or longer: 1022 6 links or longer: 42 7 links or
        Message 3 of 4 , Dec 3, 2008
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          2008/12/4 Jens Kruse Andersen <jens.k.a@...>:
          > Jarek wrote:
          >> 112511682470782472978100 = 1.12512*10^23
          >> is the only number N below 1.23056*10^23 which produces 18 primes by
          >> the formula
          >> N * 2^n +/- 1, n=0,...,8
          >
          > Congratulations on another great result!

          Thanks.

          Another LUCKY result, I would say :-) At the moment I have the
          following solution count:
          5 links or longer: 1022
          6 links or longer: 42
          7 links or longer: 3
          8 links: 1

          Given that the additional link appears in 4-5% of solutions, the
          expected nuber of 7-linked solutions is 2 and the expected number of
          8-linked solutions is around (or even slightly below) 0.1.

          Jarek
        • Robert
          ... Fantastic find, so jealous. And which, in its elemental form k=N/4=28127920617695618244525 has 2^4+k and 2^6+k prime. Robert
          Message 4 of 4 , Dec 3, 2008
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            --- In primenumbers@yahoogroups.com, "jarek372000"
            <jaroslaw.wroblewski@...> wrote:
            >
            > Yesterday I started a search aimed at 18 Simultaneous Primes (BiTwin).
            > So far I failed to improve SP18 record, but I have determined that the
            > number
            > 112511682470782472978100 = 1.12512*10^23
            > is the only number N below 1.23056*10^23 which produces 18 primes by
            > the formula
            > N * 2^n +/- 1, n=0,...,8
            >
            > Jarek
            >

            Fantastic find, so jealous.

            And which, in its elemental form k=N/4=28127920617695618244525
            has 2^4+k and 2^6+k prime.

            Robert
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