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AP19 diff 53#

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  • Jaroslaw Wroblewski
    I got it overnight: 254215977184797362303 + 53#*n, n=0..18 Yes, I was hoping to find it, but not sooner than after a few days. If I am correct this improves
    Message 1 of 4 , Feb 8, 2007
      I got it overnight:

      254215977184797362303 + 53#*n, n=0..18

      Yes, I was hoping to find it, but not sooner than after a few days.

      If I am correct this improves AP19 record:
      1.464 -> 8.408 (*10^20)

      Jarek
    • Jens Kruse Andersen
      ... Congratulations on improving my AP19 record. You now have the largest AP19 to AP24, all found since January 18.
      Message 2 of 4 , Feb 9, 2007
        Jaroslaw Wroblewski wrote:
        > 254215977184797362303 + 53#*n, n=0..18

        Congratulations on improving my AP19 record.
        You now have the largest AP19 to AP24, all found since January 18.

        http://hjem.get2net.dk/jka/math/aprecords.htm is updated.
        I verify submitted AP's and test for extensions, so others will have
        to be fast to discover something. No errors or extensions found yet.

        --
        Jens Kruse Andersen
      • Jaroslaw Wroblewski
        I was trying to get AP17 with difference 107*61#. The reason why I didn t use primorial difference is that I needed 9 primes coprime with the sequence
        Message 3 of 4 , Feb 10, 2007
          I was trying to get AP17 with difference 107*61#. The reason why I
          didn't use primorial difference is that I needed 9 primes coprime with
          the sequence difference and with product below (2^62)/15 and primes 67-103
          are the largest 9 consecutive primes with that property, so I had to
          avoid them as factors of the sequence difference.

          I was rather unlucky sitting there with 10 AP15's and nothing longer than
          that (I should have AP16 every 4-5 AP15's).

          And right now came the first sequence longer than 15 terms:

          62749659973280668140514103 + 107*61#*n, n=0..18

          I was expecting to get AP17. I was taking into acount small chance of AP18.
          But I was never thinking of AP19 of that size, so I was really surprised
          when it has appeared.

          Jarek
        • Jens Kruse Andersen
          ... Congratulations! That lucky hit is the first triple record set since the page opened in January 2005. Back then there was an existing triple record from
          Message 4 of 4 , Feb 11, 2007
            Jaroslaw Wroblewski wrote:

            > I was trying to get AP17 with difference 107*61#.
            > And right now came the first sequence longer than 15 terms:
            >
            > 62749659973280668140514103 + 107*61#*n, n=0..18

            Congratulations!
            That lucky hit is the first triple record set since the page opened in
            January 2005. Back then there was an existing triple record from 2004 to
            2006: AP21 to AP23 by Markus Frind, Paul Jobling and Paul Underwood.
            They actually searched for AP23!

            Jaroslaw now has all the largest from AP17 to AP24:
            http://hjem.get2net.dk/jka/math/aprecords.htm#records

            --
            Jens Kruse Andersen
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