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Re: FibLuc cofactors with Primo

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  • djbroadhurst
    ... I offered some harder-to-find archivable PRPs to Bernardo for proving with Primo, for joint credit. He declined. Perhaps they are too small for current
    Message 1 of 7 , Dec 22, 2011
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      --- In primeform@yahoogroups.com,
      "djbroadhurst" <d.broadhurst@...> wrote:
      >
      > Congrats to Bernardo for proving in
      > http://primes.utm.edu/primes/page.php?id=103720
      > Donovan's 7-year-old PRP at
      > http://donovanjohnson.com/fibonacci.html
      >
      > I imagine that other such easily found PRPs at
      > http://donovanjohnson.com/lucas.html
      > will soon yield to fervent users of Primo.

      I offered some harder-to-find archivable PRPs to
      Bernardo for proving with Primo, for joint credit.
      He declined. Perhaps they are too small for
      current users of Primo :-?

      Here they are, should anyone else wish to
      watch paint dry, while running ECPP:

      U(n)=fibonacci(n);

      {
      prp7053=U(33997)/(67993*1506815033*7235377529*466982112061*23455575167945633);
      prp7213=U(34607)/(1038902141*12598401493);
      prp7239=U(34807)/(6334873*10947288797*7956070560050091313);
      prp7272=U(34897)/(139589*3978257*8282523773);

      v=[prp7053,prp7213,prp7239,prp7272];
      for(k=1,#v,p=v[k];print([#Str(p),ispseudoprime(p,0)]));
      }

      [7053, 1]
      [7213, 1]
      [7239, 1]
      [7272, 1]

      David
    • Bernardo Boncompagni
      ... Thank you for your suggestion, David. I put my brand new 480-core machine at work on one of them and it managed to certify the 8273-digit candidate in
      Message 2 of 7 , Dec 23, 2011
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        >
        > I imagine that other such easily found PRPs at
        > http://donovanjohnson.com/lucas.html
        > will soon yield to fervent users of Primo.
        >
        Thank you for your suggestion, David. I put my brand new 480-core machine
        at work on one of them and it managed to certify the 8273-digit candidate
        in around 15 hours. See
        http://primes.utm.edu/top20/page.php?id=65
        for more information.


        [Non-text portions of this message have been removed]
      • djbroadhurst
        ... As predicted, Bernardo has promoted Donovan s PRP to a prime: http://primes.utm.edu/primes/page.php?id=103784 The next one on Donovan s list is
        Message 3 of 7 , Dec 24, 2011
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          --- In primeform@yahoogroups.com,
          "djbroadhurst" <d.broadhurst@...> wrote:

          > I imagine that other such easily found PRPs at
          > http://donovanjohnson.com/lucas.html
          > will soon yield to fervent users of Primo.

          As predicted, Bernardo has promoted Donovan's PRP to a prime:
          http://primes.utm.edu/primes/page.php?id=103784

          The next one on Donovan's list is
          http://donovanjohnson.com/lucas.html
          > V(39769)/(2863369*6334883549)
        • paulunderwooduk
          ... I find it hard to believe that all the larger numbers given on: http://donovanjohnson.com/lucas.html http://donovanjohnson.com/fibonacci.html were tested
          Message 4 of 7 , Dec 24, 2011
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            --- In primeform@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
            >
            > --- In primeform@yahoogroups.com,
            > "djbroadhurst" <d.broadhurst@> wrote:
            >
            > > I imagine that other such easily found PRPs at
            > > http://donovanjohnson.com/lucas.html
            > > will soon yield to fervent users of Primo.
            >
            > As predicted, Bernardo has promoted Donovan's PRP to a prime:
            > http://primes.utm.edu/primes/page.php?id=103784
            >
            > The next one on Donovan's list is
            > http://donovanjohnson.com/lucas.html
            > > V(39769)/(2863369*6334883549)
            >

            I find it hard to believe that all the larger numbers given on:
            http://donovanjohnson.com/lucas.html
            http://donovanjohnson.com/fibonacci.html
            were tested with "a Miller-Rabin primality test in 10 randomly chosen bases (ispseudoprime test in PARI/GP)." It must have taken a long time,

            Paul
          • paulunderwooduk
            ... I ran some tests on the biggest of the numbers with a 2.4Ghz core2: $ time echo ispseudoprime(fibonacci(348307)/(1393229*14759160817),1) | gp -q 1 real
            Message 5 of 7 , Dec 24, 2011
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              --- In primeform@yahoogroups.com, "paulunderwooduk" <paulunderwood@...> wrote:
              >
              >
              >
              > --- In primeform@yahoogroups.com, "djbroadhurst" <d.broadhurst@> wrote:
              > >
              > > --- In primeform@yahoogroups.com,
              > > "djbroadhurst" <d.broadhurst@> wrote:
              > >
              > > > I imagine that other such easily found PRPs at
              > > > http://donovanjohnson.com/lucas.html
              > > > will soon yield to fervent users of Primo.
              > >
              > > As predicted, Bernardo has promoted Donovan's PRP to a prime:
              > > http://primes.utm.edu/primes/page.php?id=103784
              > >
              > > The next one on Donovan's list is
              > > http://donovanjohnson.com/lucas.html
              > > > V(39769)/(2863369*6334883549)
              > >
              >
              > I find it hard to believe that all the larger numbers given on:
              > http://donovanjohnson.com/lucas.html
              > http://donovanjohnson.com/fibonacci.html
              > were tested with "a Miller-Rabin primality test in 10 randomly chosen bases (ispseudoprime test in PARI/GP)." It must have taken a long time,
              >

              I ran some tests on the biggest of the numbers with a 2.4Ghz core2:

              $ time echo "ispseudoprime(fibonacci(348307)/(1393229*14759160817),1)" | gp -q
              1

              real 56m44.939s
              user 56m41.673s
              sys 0m1.692s

              Next my own 2-selfridge algorithm ( which is currently verified for n<6.2*10^11), which is stored in my .bashrc file and pipes into gp -q:

              $ time S1 fibonacci\(348307\)/\(1393229*14759160817\)
              LIKELYprime

              real 114m9.782s
              user 112m59.832s
              sys 0m6.720s

              Then I ran some PFGW tests:

              $ time ./pfgw64 -q"F(348307)/(1393229*14759160817)"
              PFGW Version 3.4.4.64BIT.20101104.x86_Dev [GWNUM 26.4]

              F(348307)/(1393229*14759160817) is 3-PRP! (544.9254s+0.0110s) 1/28.00

              real 9m4.948s
              user 6m56.506s
              sys 0m0.100s

              $ time ./pfgw64 -tp -q"F(348307)/(1393229*14759160817)"
              PFGW Version 3.4.4.64BIT.20101104.x86_Dev [GWNUM 26.4]

              Primality testing F(348307)/(1393229*14759160817) [N+1, Brillhart-Lehmer-Selfridge]
              Running N+1 test using discriminant 7, base 7+sqrt(7)
              Calling Brillhart-Lehmer-Selfridge with factored part 0.01%
              F(348307)/(1393229*14759160817) is Lucas PRP! (2034.5473s+0.0111s)

              real 33m54.567s
              user 25m4.678s
              sys 0m2.004s

              $ time ./pfgw64 -tc -q"F(348307)/(1393229*14759160817)"
              PFGW Version 3.4.4.64BIT.20101104.x86_Dev [GWNUM 26.4]

              Primality testing F(348307)/(1393229*14759160817) [N-1/N+1, Brillhart-Lehmer-Selfridge]
              Running N-1 test using base 7
              Running N+1 test using discriminant 23, base 3+sqrt(23)
              Calling N-1 BLS with factored part 0.01% and helper 0.01% (0.04% proof)
              F(348307)/(1393229*14759160817) is Fermat and Lucas PRP! (2702.0909s+0.0114s)

              real 45m2.111s
              user 32m20.409s
              sys 0m3.904s

              So if my 2-selfridge algorithm was implemented in PFGW it would take ~14 minutes for this number,

              Paul
            • djbroadhurst
              ... Larry Soule and Predrag Minovic have promoted a larger of Donovan s finds: http://primes.utm.edu/primes/page.php?id=105913#comments David
              Message 6 of 7 , Mar 29, 2012
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                --- In primeform@yahoogroups.com,
                "djbroadhurst" <d.broadhurst@...> wrote:

                > As predicted, Bernardo has promoted Donovan's PRP to a prime:
                > http://primes.utm.edu/primes/page.php?id=103784

                Larry Soule and Predrag Minovic have promoted a larger
                of Donovan's finds:

                http://primes.utm.edu/primes/page.php?id=105913#comments

                David
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