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AP21

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  • 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 1 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 2 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 3 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 4 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 5 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 6 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 7 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 8 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 9 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 10 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 11 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 12 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 13 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 14 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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