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Another AP21

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  • Jaroslaw Wroblewski
    I just got another AP21: 1245653020090313 + 384*37#*n, n=0..20 This improves my previous AP21: 52.379P - 58.236P where P=10^15. Jarek ~
    Message 1 of 16 , Feb 4, 2007
      I just got another AP21:

      1245653020090313 + 384*37#*n, n=0..20

      This improves my previous AP21:
      52.379P -> 58.236P
      where P=10^15.

      Jarek
      ~
    • 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 2 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 3 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 4 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 5 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 6 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 7 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 8 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 9 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 10 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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