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Second titanic AP9

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  • paulunderwooduk
    We have found another, slightly larger, AP9: http://primes.utm.edu/primes/page.php?id=103845 Paul
    Message 1 of 9 , Jan 2, 2012
      We have found another, slightly larger, AP9:
      http://primes.utm.edu/primes/page.php?id=103845

      Paul
    • djbroadhurst
      ... Congrats! You forgot to add hash to http://primes.utm.edu/bios/page.php?id=339 ... David
      Message 2 of 9 , Jan 3, 2012
        --- In primeform@yahoogroups.com,
        "paulunderwooduk" <paulunderwood@...> wrote:
        >
        > We have found another, slightly larger, AP9:
        > http://primes.utm.edu/primes/page.php?id=103845

        Congrats! You forgot to add hash to
        http://primes.utm.edu/bios/page.php?id=339
        > We are examining k*2371+1,
        > k is in the range {50000000000, 94000000000}

        David
      • paulunderwooduk
        ... Fixed. Thanks. The remarkable thing about this AP9 is that it was extended from an AP5 which was detected in the range -- the 4 upper terms came from
        Message 3 of 9 , Jan 3, 2012
          --- In primeform@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
          >
          > --- In primeform@yahoogroups.com,
          > "paulunderwooduk" <paulunderwood@> wrote:
          > >
          > > We have found another, slightly larger, AP9:
          > > http://primes.utm.edu/primes/page.php?id=103845
          >
          > Congrats! You forgot to add hash to
          > http://primes.utm.edu/bios/page.php?id=339
          > > We are examining k*2371+1,
          > > k is in the range {50000000000, 94000000000}
          >

          Fixed. Thanks.

          The remarkable thing about this AP9 is that it was extended from an AP5 which was detected in the range -- the 4 upper terms came from extending.

          Paul
        • Jens Kruse Andersen
          ... Congratulations! http://users.cybercity.dk/~dsl522332/math/aprecords.htm is updated. -- Jens Kruse Andersen
          Message 4 of 9 , Jan 3, 2012
            Paul wrote:
            > We have found another, slightly larger, AP9:
            > http://primes.utm.edu/primes/page.php?id=103845

            Congratulations!
            http://users.cybercity.dk/~dsl522332/math/aprecords.htm is updated.

            --
            Jens Kruse Andersen
          • djbroadhurst
            ... Congrats to Paul and Ken on 5 titanic AP9s: 116040452086*2371#+1 1014 p308 Jan 2012 AP (9,d=6317280828*2371#) 97336164242*2371#+1 1014 p308 Apr 2013 AP
            Message 5 of 9 , Apr 12, 2013
              Paul wrote:

              > We have found another, slightly larger, AP9:
              > http://primes.utm.edu/primes/page.php?id=103845

              Congrats to Paul and Ken on 5 titanic AP9s:

              116040452086*2371#+1 1014 p308 Jan 2012 AP (9,d=6317280828*2371#)
              97336164242*2371#+1 1014 p308 Apr 2013 AP (9,d=6350457699*2371#)
              93537753980*2371#+1 1014 p308 Apr 2013 AP (9,d=3388165411*2371#)
              92836168856*2371#+1 1014 p308 Apr 2013 AP (9,d= 127155673*2371#)
              69318339141*2371#+1 1014 p308 Jul 2011 AP (9,d=1298717501*2371#)

              David
            • paulunderwooduk
              ... Thanks David. Ken looked non-exhaustively for AP5s of k between 40 billion and 61 billion, for k*2371#+1; I exhaustively searched for AP5s between 61
              Message 6 of 9 , Apr 12, 2013
                --- In primeform@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
                >
                >
                >
                > Paul wrote:
                >
                > > We have found another, slightly larger, AP9:
                > > http://primes.utm.edu/primes/page.php?id=103845
                >
                > Congrats to Paul and Ken on 5 titanic AP9s:
                >
                > 116040452086*2371#+1 1014 p308 Jan 2012 AP (9,d=6317280828*2371#)
                > 97336164242*2371#+1 1014 p308 Apr 2013 AP (9,d=6350457699*2371#)
                > 93537753980*2371#+1 1014 p308 Apr 2013 AP (9,d=3388165411*2371#)
                > 92836168856*2371#+1 1014 p308 Apr 2013 AP (9,d= 127155673*2371#)
                > 69318339141*2371#+1 1014 p308 Jul 2011 AP (9,d=1298717501*2371#)
                >

                Thanks David.

                Ken looked non-exhaustively for AP5s of k between 40 billion and 61 billion, for k*2371#+1; I exhaustively searched for AP5s between 61 billion and 94 billion. Here is a count of what I found:
                AP5 1,020,833,527
                AP6 7,270,362
                AP7 63,368
                AP8 336
                AP9 5
                (Not disjoint.)

                The time taken by us was:
                1 GHz year sieving with NewPGen
                35 GHz years PRPing with pfgw64
                82 GHz years searching the data set
                0.5 GHz years extending APs with pfgw64
                (Based on AMD Barcelona cores.)

                Here are links to first known AP lengths 5 to 8:
                AP5 https://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0002&L=NMBRTHRY&P=R632&1=NMBRTHRY&9=A&J=on&d=No+Match%3BMatch%3BMatches&z=4
                AP6 https://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0005&L=NMBRTHRY&P=R42&1=NMBRTHRY&9=A&J=on&d=No+Match%3BMatch%3BMatches&z=4
                AP7 http://tech.groups.yahoo.com/group/primenumbers/message/5976
                AP8 https://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0306&L=NMBRTHRY&P=R410&1=NMBRTHRY&9=A&J=on&d=No+Match%3BMatch%3BMatches&z=4

                The data, scripts and programs used by us are available on request.

                Primeform e-group has a healthy position on:
                http://primes.utm.edu/bios/top20.php?type=project&by=PrimesRank

                Paul
              • paulunderwooduk
                ... The lower bound should read 50 billion, Paul
                Message 7 of 9 , Apr 12, 2013
                  --- In primeform@yahoogroups.com, "paulunderwooduk" <paulunderwood@...> wrote:

                  > Ken looked non-exhaustively for AP5s of k between 40 billion and 61 billion, for k*2371#+1;

                  The lower bound should read 50 billion,

                  Paul
                • djbroadhurst
                  ... That was what impressed me most. ... by your strategy of massive uploads of transiently listable AP8s, perfectly according to the rules. Neat job, all
                  Message 8 of 9 , Apr 12, 2013
                    --- In primeform@yahoogroups.com,
                    "paulunderwooduk" <paulunderwood@...> wrote:

                    > 82 GHz years searching the data set

                    That was what impressed me most.

                    > Primeform e-group has a healthy position on:
                    > http://primes.utm.edu/bios/top20.php?type=project&by=PrimesRank

                    I guess that Ken has achieved his secondary ambition:
                    > number ever on any list: 1930
                    by your strategy of massive uploads of transiently
                    listable AP8s, perfectly according to the rules.

                    Neat job, all round!

                    David
                  • paulunderwooduk
                    ... Ken used several computers for his part. I used POSIX threads, acting on a 5.5GB bit map, on a 16 core box. ... All done! Ken and I submitted 2850 primes
                    Message 9 of 9 , Apr 13, 2013
                      --- In primeform@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
                      >
                      > --- In primeform@yahoogroups.com,
                      > "paulunderwooduk" <paulunderwood@> wrote:
                      >
                      > > 82 GHz years searching the data set
                      >
                      > That was what impressed me most.
                      >

                      Ken used several computers for his part. I used POSIX threads, acting on a 5.5GB bit map, on a 16 core box.

                      > > Primeform e-group has a healthy position on:
                      > > http://primes.utm.edu/bios/top20.php?type=project&by=PrimesRank
                      >
                      > I guess that Ken has achieved his secondary ambition:
                      > > number ever on any list: 1930
                      > by your strategy of massive uploads of transiently
                      > listable AP8s, perfectly according to the rules.
                      >

                      All done! Ken and I submitted 2850 primes under The Prime Pages prover code p308.

                      egroup's page has been updated:
                      http://primes.utm.edu/bios/page.php?id=339

                      It's going to be a big task to get a titanic AP10 of primes with average luck ;-)

                      Paul
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