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AP21

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  • Jaroslaw Wroblewski
    Last year I have started a search for AP21 with difference k*37#, k
    Message 1 of 16 , Jan 1, 2007
      Last year I have started a search for AP21 with difference
      k*37#, k<=40.
      I used 15*PentiumD805(64bits/2threads)+14*Athlon64
      +30*Athlon2500+15*Duron900

      I had to wait till this year (about 18 hours) for the first
      AP with at least 20 terms and this is a 21:

      9358091177025961 + 11*37#*n, n=0...20

      The largest term has 17 digits: 10990653566684161

      It was found by one of the Durons. On my program a Duron is
      about 13 times less efficient than combined 2 threads
      of a PentiumD.

      Jarek
    • Jens Kruse Andersen
      ... Congratulations again! http://hjem.get2net.dk/jka/math/aprecords.htm is updated with the largest known AP21. That was fast to start the news section for
      Message 2 of 16 , Jan 1, 2007
        Jaroslaw Wroblewski wrote:
        > 9358091177025961 + 11*37#*n, n=0...20

        Congratulations again!
        http://hjem.get2net.dk/jka/math/aprecords.htm is
        updated with the largest known AP21.
        That was fast to start the news section for 2007.

        --
        Jens Kruse Andersen
      • Jaroslaw Wroblewski
        I just got 620353098196661 + 84*37#*n, n=0..20 This improves largest known AP21 10.99P - 13.087P, where P=10^15. Jarek
        Message 3 of 16 , Feb 3, 2007
          I just got

          620353098196661 + 84*37#*n, n=0..20

          This improves largest known AP21
          10.99P -> 13.087P, where P=10^15.

          Jarek
        • Jaroslaw Wroblewski
          I just got 789337428437009 + 320*37#*n, n=0..21 This improves largest known AP21: 13.087P - 50.656P AP22: 5.734P - 50.656P where P=10^15. Jarek
          Message 4 of 16 , Feb 4, 2007
            I just got

            789337428437009 + 320*37#*n, n=0..21

            This improves largest known
            AP21: 13.087P -> 50.656P
            AP22: 5.734P -> 50.656P
            where P=10^15.

            Jarek
          • 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 5 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 6 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 7 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 8 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 9 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 10 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 11 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 12 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 13 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 14 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 15 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 16 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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