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large AP4

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  • djbroadhurst
    ... Here, eventually, is my reply: Calling Brillhart-Lehmer-Selfridge with factored part 31.24% 3*164196977*2^80000-1631979959*2^25001-1 is Lucas PRP!
    Message 1 of 11 , Oct 24, 2010
      --- In primeform@yahoogroups.com,
      "mikeoakes2" <mikeoakes2@...> wrote:

      > Here is a new AP4 record at 15004 digits:-
      > (1000362700+2571033*n)*34687#+1 is prime for n=0..3

      Here, eventually, is my reply:

      Calling Brillhart-Lehmer-Selfridge with factored part 31.24%
      3*164196977*2^80000-1631979959*2^25001-1 is Lucas PRP! (103.0930s+0.0038s)

      Calling Brillhart-Lehmer-Selfridge with factored part 31.40%
      164196977*2^80001-1631979959*2^25000-1 is Lucas PRP! (99.0570s+0.0044s)

      Calling Brillhart-Lehmer-Selfridge with factored part 99.97%
      164196977*2^80000-1 is prime! (30.1911s+0.0057s)

      Calling Brillhart-Lehmer-Selfridge with factored part 99.88%
      1631979959*2^25000-1 is prime! (2.4893s+0.0047s)

      The two largest elements of this AP4, with 24092 and 24091 digits,
      were proven prime using the method of Konyagin and Pomerance.

      David Broadhurst, 24 October 2010
    • Jens Kruse Andersen
      ... Congratulations on a large record improvement. http://users.cybercity.dk/~dsl522332/math/aprecords.htm is updated. -- Jens Kruse Andersen
      Message 2 of 11 , Oct 25, 2010
        David Broadhurst wrote:
        > 3*164196977*2^80000-1631979959*2^25001-1 is Lucas PRP!
        > 164196977*2^80001-1631979959*2^25000-1 is Lucas PRP!
        > 164196977*2^80000-1 is prime!
        > 1631979959*2^25000-1 is prime!
        >
        > The two largest elements of this AP4, with 24092 and 24091 digits,
        > were proven prime using the method of Konyagin and Pomerance.

        Congratulations on a large record improvement.
        http://users.cybercity.dk/~dsl522332/math/aprecords.htm is updated.

        --
        Jens Kruse Andersen
      • mikeoakes2
        ... David Many congratulations on your big new record. You don t say what effort was involved. For comparison, I ve checked what numbers my hash technology
        Message 3 of 11 , Oct 30, 2010
          --- In primeform@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
          >
          > --- In primeform@yahoogroups.com,
          > "mikeoakes2" <mikeoakes2@> wrote:
          >
          > > Here is a new AP4 record at 15004 digits:-
          > > (1000362700+2571033*n)*34687#+1 is prime for n=0..3
          >
          > Here, eventually, is my reply:
          >
          > Calling Brillhart-Lehmer-Selfridge with factored part 31.24%
          > 3*164196977*2^80000-1631979959*2^25001-1 is Lucas PRP! (103.0930s+0.0038s)
          >
          > Calling Brillhart-Lehmer-Selfridge with factored part 31.40%
          > 164196977*2^80001-1631979959*2^25000-1 is Lucas PRP! (99.0570s+0.0044s)
          >
          > Calling Brillhart-Lehmer-Selfridge with factored part 99.97%
          > 164196977*2^80000-1 is prime! (30.1911s+0.0057s)
          >
          > Calling Brillhart-Lehmer-Selfridge with factored part 99.88%
          > 1631979959*2^25000-1 is prime! (2.4893s+0.0047s)
          >
          > The two largest elements of this AP4, with 24092 and 24091 digits,
          > were proven prime using the method of Konyagin and Pomerance.

          David
          Many congratulations on your big new record.

          You don't say what effort was involved.
          For comparison, I've checked what numbers my "hash" technology would require for a record of this size, for a "vanilla" detection algorithm, i.e. without any Ken-type extension tricks.

          k=4 q=55793
          M1=19890161. M2=39780323.
          digits: 24094.885
          score=80.718039
          PRP'ing: 15.818496 GHz-yrs (100.00000%)
          APk-detection: 0.000000012682880 GHz-yrs (0.000000080177533%)
          Total: 15.818496 GHz-yrs
          APk counts:-
          k=1 c=6980.6133
          k=2 c=24364481.
          k=3 c=4275.4493
          k=4 c=1.0003326
          k=5 c=0.00026330492

          Here is the output from the same program for your AP3 record:-

          k=3 q=367453
          M1=4077056.1 M2=8154112.1 c=1.0000511
          digits: 159381.72
          score=83.853401
          PRP'ing: 163.82127 GHz-yrs (100.00000%)
          APk-detection: 2.2318013 E-11 GHz-yrs (1.3623391 E-11%)
          Total: 163.82127 GHz-yrs
          APk counts:-
          k=1 c=253.59636
          k=2 c=32155.557
          k=3 c=1.0000511
          k=4 c=0.000041469329

          I wonder how those PRP'ing estimates compare with your actual figures, and in particular, whether the AP3 record was about 10 times as burdensome? (It has a considerably higher "score".)

          Mike
        • djbroadhurst
          ... I estimated the time for a Poisson mean of 1.0 at about half of that, but I m not telling just how unlucky I was, in fact :-( Please note that the cost of
          Message 4 of 11 , Oct 30, 2010
            --- In primeform@yahoogroups.com,
            "mikeoakes2" <mikeoakes2@...> wrote:

            > For comparison, I've checked what numbers my "hash"
            > technology would require for a record of this size,
            > for a "vanilla" detection algorithm
            > Total: 15.818496 GHz-yrs

            I estimated the time for a Poisson mean of 1.0
            at about half of that, but I'm not telling
            just how unlucky I was, in fact :-(

            Please note that the cost of my big database of 25000-bit
            primes is not included, since this had already been amortized
            over several previous records, one going back to 2005:
            http://primes.utm.edu/primes/page.php?id=73546
            The key to my method was to recycle primes with only
            31% of the digits of the largest member of the new AP4.
            You can work out, from past CHG performance, how much
            higher this recycling might take one :-)

            > whether the AP3 record was about 10 times as burdensome?

            Not for me, since here I merely stole the all the AP2s from
            the public database :-)

            David
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