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Re: [primeform] AP20

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  • Jaroslaw Wroblewski
    I just got 19-digit AP20 2962411312104427 + 185*41#*n, n=0..19 Jarek
    Message 1 of 16 , Feb 7, 2007
      I just got 19-digit AP20

      2962411312104427 + 185*41#*n, n=0..19

      Jarek
    • 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 2 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 3 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 4 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 5 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 6 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 7 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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