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Re: [primeform] AP21

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  • Jaroslaw Wroblewski
    I just got 3135462279378283 + 316*37#*n, n=0..21 This improves my previous AP21 and AP22: 50.656P - 52.379P where P=10^15. Jarek
    Message 1 of 16 , Feb 4, 2007
      I just got

      3135462279378283 + 316*37#*n, n=0..21

      This improves my previous AP21 and AP22:
      50.656P -> 52.379P
      where P=10^15.

      Jarek
    • Jens Kruse Andersen
      ... Congratulations. http://hjem.get2net.dk/jka/math/aprecords.htm is updated. This combined AP21/AP22 record ended a 4-day period (the first) where no AP was
      Message 2 of 16 , Feb 4, 2007
        Jaroslaw Wroblewski wrote:
        > 789337428437009 + 320*37#*n, n=0..21

        Congratulations.
        http://hjem.get2net.dk/jka/math/aprecords.htm is updated.

        This combined AP21/AP22 record ended a 4-day period (the first) where no
        AP was the largest known for two lengths.

        --
        Jens Kruse Andersen
      • 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 3 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 4 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 5 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 6 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 7 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 8 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 9 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 10 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 11 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 12 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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