Loading ...
Sorry, an error occurred while loading the content.
 

AP20

Expand Messages
  • 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 1 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 2 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 3 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 4 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 5 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 6 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 7 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 8 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
                  Your message has been successfully submitted and would be delivered to recipients shortly.