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20-digit AP21

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  • Jaroslaw Wroblewski
    I just got the following sequence 1925228725347080393 + 47#*n, n=0..20 with 20-digit last term: 14223024377116908593. I was aiming at AP20 and was surprised to
    Message 1 of 16 , Feb 7, 2007
      I just got the following sequence

      1925228725347080393 + 47#*n, n=0..20

      with 20-digit last term: 14223024377116908593.

      I was aiming at AP20 and was surprised to get an AP21.

      Jarek
    • David Broadhurst
      ... I do find your messages exciting, Jarek. Please continiue updating us like this. [... fumbles for nonsensical, ungrammatical, Polish phrase ...] Gratulacj
      Message 2 of 16 , Feb 7, 2007
        --- In primeform@yahoogroups.com, Jaroslaw Wroblewski
        <Jaroslaw.Wroblewski@...> wrote:

        > I just got the following sequence
        > 1925228725347080393 + 47#*n, n=0..20
        > with 20-digit last term: 14223024377116908593.
        > I was aiming at AP20 and was surprised to get an AP21.

        I do find your messages exciting, Jarek.
        Please continiue updating us like this.

        [... fumbles for nonsensical, ungrammatical,
        Polish phrase ...]

        Gratulacj na waszej niedawnej dobrej pracy

        David
      • Jens Kruse Andersen
        ... Congratulations on your 7th AP21 record in 2007 - and the 6th since Sunday! http://hjem.get2net.dk/jka/math/aprecords.htm#history21 A 20-digit AP21 with
        Message 3 of 16 , Feb 8, 2007
          Jaroslaw Wroblewski wrote:
          > I just got the following sequence
          > 1925228725347080393 + 47#*n, n=0..20
          > with 20-digit last term: 14223024377116908593.
          > I was aiming at AP20 and was surprised to get an AP21.

          Congratulations on your 7th AP21 record in 2007
          - and the 6th since Sunday!
          http://hjem.get2net.dk/jka/math/aprecords.htm#history21
          A 20-digit AP21 with primorial difference is impressive.
          As you know, the difference is too large for
          http://hjem.get2net.dk/jka/math/simultprime.htm

          --
          Jens Kruse Andersen
        • Jaroslaw Wroblewski
          ... Unfortunately this result hits 2^64 limit. I can continue higher, but my search is going to be much less efficient. I will try AP19 with the difference 53#
          Message 4 of 16 , Feb 8, 2007
            David Broadhurst wrote:

            > I do find your messages exciting, Jarek.
            > Please continiue updating us like this.

            Unfortunately this result hits 2^64 limit. I can continue higher, but
            my search is going to be much less efficient. I will try AP19 with
            the difference 53# now.

            > [... fumbles for nonsensical, ungrammatical,
            > Polish phrase ...]

            > Gratulacj na waszej niedawnej dobrej pracy

            Dziekuje.

            Jens Kruse Andersen wrote:

            > Congratulations on your 7th AP21 record in 2007
            > - and the 6th since Sunday!

            Thanks. I had a lot of fun working on this. And ceratinly I had a lot of
            luck with some of my findings. Quite often I was getting results much
            sooner than I had expected.

            Thank you for keeping and updating your page - without it hunting large
            AP's wouldn't make much sense.

            > A 20-digit AP21 with primorial difference is impressive.

            I wasn't taking finding AP21 there into account, otherwise I would have
            written the program differently. In fact I shouldn't even get an AP20
            with the difference 47# so quickly.

            > As you know, the difference is too large for
            > http://hjem.get2net.dk/jka/math/simultprime.htm

            Yes, I am well aware of that. My program is working with the assumption of
            fixed difference and a primorial is the best choice. To increase the
            search area I was adding a factor to it, but for 47# and higher, the
            search area is larger than I can go through, so I have no reason to
            select a non-primorial difference.

            Jarek
          • drastichs
            ... It seems, that in fact this is longer sequence of prime numbers, than you have already thought about. According to my results, numbers
            Message 5 of 16 , Feb 8, 2007
              --- In primeform@yahoogroups.com, Jaroslaw Wroblewski
              <Jaroslaw.Wroblewski@...> wrote:
              >
              > I just got the following sequence
              >
              > 1925228725347080393 + 47#*n, n=0..20
              >
              > with 20-digit last term: 14223024377116908593.
              >
              > I was aiming at AP20 and was surprised to get an AP21.
              >
              > Jarek
              >

              It seems, that in fact this is "longer" sequence of prime numbers,
              than you have already thought about.
              According to my results, numbers

              1310338942758588983 = 1925228725347080393 - 47# is prime as well

              and furthermore also

              695449160170097573 = 1925228725347080393 - 2*47# is prime!

              This is really the end of prime sequence going "down", because the
              next one is

              80559377581606163 = 78218141 * 1029932143

              Thus Jaroslaw has found AP23 starting at 695449160170097573 +
              47#*n,n=0..22

              Is there any mistake involved in my thoughts?

              Stanislav Drastich
            • Jaroslaw Wroblewski
              ... I am getting the following factorizations: 1310338942758588983 {{6323, 1}, {207233740749421, 1}} 695449160170097573 {{2357, 1}, {4567, 1}, {4597, 1},
              Message 6 of 16 , Feb 8, 2007
                > It seems, that in fact this is "longer" sequence of prime numbers,
                > than you have already thought about.
                > According to my results, numbers
                >
                > 1310338942758588983 = 1925228725347080393 - 47# is prime as well
                >
                > and furthermore also
                >
                > 695449160170097573 = 1925228725347080393 - 2*47# is prime!
                >
                > This is really the end of prime sequence going "down", because the
                > next one is
                >
                > 80559377581606163 = 78218141 * 1029932143
                >

                I am getting the following factorizations:

                1310338942758588983
                {{6323, 1}, {207233740749421, 1}}

                695449160170097573
                {{2357, 1}, {4567, 1}, {4597, 1}, {14054011, 1}}

                80559377581606163
                {{59, 1}, {83, 1}, {210319, 1}, {78218141, 1}}

                Jarek
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