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Re: [primeform] Another AP21

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  • Jaroslaw Wroblewski
    I just got 25521343898340097 + 37*41#*n, n=0..20 This improves AP21 record: 58.236P - 250.666P and misses AP20 record of 260.307P Jarek
    Message 1 of 16 , Feb 5, 2007
      I just got

      25521343898340097 + 37*41#*n, n=0..20

      This improves AP21 record:
      58.236P -> 250.666P
      and misses AP20 record of 260.307P

      Jarek
    • Jaroslaw Wroblewski
      I just got 2036800114407689 + 66*41#*n, n=0..19 This improves AP20 record: 260.307P - 383.566P For n=-2,-1 the formula gives negative primes. Jarek
      Message 2 of 16 , Feb 6, 2007
        I just got

        2036800114407689 + 66*41#*n, n=0..19

        This improves AP20 record:
        260.307P -> 383.566P

        For n=-2,-1 the formula gives negative primes.

        Jarek
      • Jaroslaw Wroblewski
        I just got 19-digit AP20 2962411312104427 + 185*41#*n, n=0..19 Jarek
        Message 3 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 4 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 5 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 6 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 7 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 8 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 9 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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