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AP19 starting with 19

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  • Jaroslaw Wroblewski
    Wojciech Izykowski has discovered AP19 with the smallest possible start of 19: 19 + 13234551541698967679 * 17# * n, n=0,...,18 (27 digits) At the moment it is
    Message 1 of 6 , Feb 25, 2013
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      Wojciech Izykowski has discovered AP19 with the smallest possible start of 19:

      19 + 13234551541698967679 * 17# * n, n=0,...,18
      (27 digits)

      At the moment it is not known whether the difference of the AP is the
      smallest possible, but Wojciech is working to determine that.

      Although Wojciech was using the ideas I have developed in the past, he
      created brand new implementation of the search program on his own.

      Jarek
    • mikeoakes2
      ... An amazing and highly nontrivial discovery - many congratulations! But don t rush to look for an AP23: heuristics in my NMBRTHRY post of 2001
      Message 2 of 6 , Feb 26, 2013
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        --- In primenumbers@yahoogroups.com, Jaroslaw Wroblewski <jaroslaw.wroblewski@...> wrote:
        >
        > Wojciech Izykowski has discovered AP19 with the smallest possible start of 19:
        >
        > 19 + 13234551541698967679 * 17# * n, n=0,...,18
        > (27 digits)
        >

        An amazing and highly nontrivial discovery - many congratulations!

        But don't rush to look for an AP23:
        heuristics in my NMBRTHRY post of 2001
        https://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0106&L=NMBRTHRY&F=&S=&P=3812
        indicate that a complete search would take many times the age of the Universe.

        Mike
      • Jens Kruse Andersen
        ... Congratulations to Wojciech! http://users.cybercity.dk/~dsl522332/math/aprecords.htm#minimalstart is updated with a mixed color entry to show that it has
        Message 3 of 6 , Feb 27, 2013
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          Jaroslaw Wroblewski wrote:
          > Wojciech Izykowski has discovered AP19 with the smallest possible start of
          > 19:
          >
          > 19 + 13234551541698967679 * 17# * n, n=0,...,18
          > (27 digits)
          >
          > At the moment it is not known whether the difference of the AP is the
          > smallest possible, but Wojciech is working to determine that.

          Congratulations to Wojciech!

          http://users.cybercity.dk/~dsl522332/math/aprecords.htm#minimalstart
          is updated with a mixed color entry to show that it has the smallest
          possible start but the difference may not be the smallest.

          --
          Jens Kruse Andersen
        • Jaroslaw Wroblewski
          Wojciech Izykowski has discovered AP19 with the smallest possible start of 19 and a smaller difference than in his first example: 19 + 4244193265542951705 *
          Message 4 of 6 , Apr 5, 2013
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            Wojciech Izykowski has discovered AP19 with the smallest possible
            start of 19 and a smaller difference than in his first example:

            19 + 4244193265542951705 * 17# * n, n=0,...,18
            (26 digits)

            He needs about a week to determine whether this difference is the
            smallest possible.

            Jarek

            2013/2/26 Jaroslaw Wroblewski <jwr@...>:
            > Wojciech Izykowski has discovered AP19 with the smallest possible start of 19:
            >
            > 19 + 13234551541698967679 * 17# * n, n=0,...,18
            > (27 digits)
            >
            > At the moment it is not known whether the difference of the AP is the
            > smallest possible, but Wojciech is working to determine that.
            >
            > Although Wojciech was using the ideas I have developed in the past, he
            > created brand new implementation of the search program on his own.
            >
            > Jarek
          • Jaroslaw Wroblewski
            ... Wojciech has completed his computations and confirmed that the above AP19 has the smallest possible diffrence among all AP19 starting with 19. Jarek
            Message 5 of 6 , Apr 10, 2013
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              2013/4/5 Jaroslaw Wroblewski <jwr@...>:
              > Wojciech Izykowski has discovered AP19 with the smallest possible
              > start of 19 and a smaller difference than in his first example:
              >
              > 19 + 4244193265542951705 * 17# * n, n=0,...,18
              > (26 digits)

              Wojciech has completed his computations and confirmed that the above
              AP19 has the smallest possible diffrence among all AP19 starting with
              19.

              Jarek
            • Jens Kruse Andersen
              ... Congratulations to Wojciech. http://users.cybercity.dk/~dsl522332/math/aprecords.htm#minimalstart is updated so the color is no longer red. It should also
              Message 6 of 6 , Apr 10, 2013
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                Jaroslaw Wroblewski wrote:
                >> 19 + 4244193265542951705 * 17# * n, n=0,...,18
                >
                > Wojciech has completed his computations and confirmed that the above
                > AP19 has the smallest possible diffrence among all AP19 starting with
                > 19.

                Congratulations to Wojciech.
                http://users.cybercity.dk/~dsl522332/math/aprecords.htm#minimalstart is
                updated so the color is no longer red.
                It should also be submitted to http://oeis.org/A061558

                --
                Jens Kruse Andersen
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