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RE: [PrimeNumbers] Some Benchmark Primality Test

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  • cino hilliard
    Try (00:25:59) gp ispseudoprime(31838235*2^29717+1) %129 = 1 (00:33:39) gp ## *** last result computed in 6mn, 29,015 ms. (17:33:32) gp
    Message 1 of 5 , Sep 1, 2009
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      Try
      (00:25:59) gp > ispseudoprime(31838235*2^29717+1)
      %129 = 1
      (00:33:39) gp > ##
      *** last result computed in 6mn, 29,015 ms.





      (17:33:32) gp > isprime(31838235*2^29717+1)
      %74 = 1
      (18:35:16) gp > ##
      *** last result computed in 51mn, 53,938 ms.



      c:\pfgw>pfgw -tc -q31838235*2^^29717+1
      PFGW Version 20090725.Win_Dev (Beta 'caveat utilitor') [GWNUM 25.12]

      Primality testing 31838235*2^29717+1 [N-1/N+1, Brillhart-Lehmer-Selfridge]
      Running N-1 test using base 17
      Running N-1 test using base 23
      Running N+1 test using discriminant 31, base 10+sqrt(31)
      Calling N-1 BLS with factored part 100.00% and helper 0.07% (300.08% proof)
      31838235*2^29717+1 is prime! (15.3991s+0.0311s)



      This 8954 digit number will be the top primo candidate if you have the time

      So before you do primo, do pfgw -tc



      pfgw ROCKS!



      Cino







      To: primenumbers@yahoogroups.com
      From: calimero22@...
      Date: Mon, 31 Aug 2009 20:05:01 +0000
      Subject: [PrimeNumbers] Some Benchmark Primality Test






      I post some time test for a primality or pseudoprimality check.

      Tests on AMD Sempron 3000+ (1800 Mhz) WIndows XP
      n=31838235*2^29717+1 digits: 8954
      Tests run by GIOVANNI DI MARIA - email: calimero22@...
      Tests give at least a Pseudoprimality PRP.

      ===================================================================
      GMP Library
      mpz_probab_prime_p(n,r) r=1 = 72 secs.
      mpz_probab_prime_p(n,r) r=0 = 34 secs.
      fermat (mpz_powm(2,n,n) = 2^n MOD n = 34 secs.
      My implementation Fermat algorytm = 33 secs.
      ===================================================================
      PFGW
      pfgw 3.2.2 (On AMD 1800 Mhz) = 3.1 secs.
      pfgw 3.2.2 (On INTEL P4 1800 Mhz) = 1.7 secs. <-----
      ===================================================================
      MATHEMATICA
      Mathematica PowerMod[2,n,n] (Fermat) = 38 secs.
      PrimeQ[n] = 157 secs.
      ===================================================================
      PARI/GP
      ispseudoprime(n) BPSW test = 130 secs.
      ispseudoprime(n,1) strong Rabin-Miller test for 1 base = 43 secs.
      powermod(x,k,m)=lift(Mod(x,m)^k) --> powermod(2,n,n) = 42 secs.
      isprime(n) = too long
      ===================================================================
      PROTH.EXE
      Normal Test = 5 secs.
      ===================================================================
      LLR.EXE
      Normal Test = 7 secs.
      ===================================================================
      PRP.EXE
      Normal Test = 7 secs.
      ===================================================================
      PrimeForm.EXE
      Normal Test = 24 secs.
      ===================================================================










      [Non-text portions of this message have been removed]
    • djbroadhurst
      ... OK ... Using ECPP to re-prove a prime already proven by BLS would be an exercise in fatuity. David
      Message 2 of 5 , Sep 1, 2009
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        --- In primenumbers@yahoogroups.com,
        cino hilliard <hillcino368@...> wrote:

        > 31838235*2^29717+1 is prime! (15.3991s+0.0311s)

        OK

        > This 8954 digit number will be the top primo candidate
        > if you have the time

        Using ECPP to re-prove a prime already proven by BLS
        would be an exercise in fatuity.

        David
      • cino hilliard
        Hi David, ... anayway, I thought we were benchmarking in this last post? I am still curious how long it would take primo to prove 31838235*2^29717+1 is prime.
        Message 3 of 5 , Sep 1, 2009
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          Hi David,



          >So before you do primo, do pfgw -tc


          anayway, I thought we were benchmarking in this last post?



          I am still curious how long it would take primo to prove 31838235*2^29717+1 is prime.

          At fiirst, I thought time was proportional to the number of digits but now I realize
          that ain't so. "When in doubt, specialize"



          Not all lost though. I learned a new word.



          I tried pfgw on the primo top entry of the top 20.



          http://www.ellipsa.eu/public/primo/top20.html



          c:\pfgw>pfgw -tc -q2^^29727+20273
          PFGW Version 20090725.Win_Dev (Beta 'caveat utilitor') [GWNUM 25.12]

          Primality testing 2^29727+20273 [N-1/N+1, Brillhart-Lehmer-Selfridge]
          Running N-1 test using base 11
          Running N+1 test using discriminant 19, base 9+sqrt(19)
          Calling N+1 BLS with factored part 0.08% and helper 0.07% (0.30% proof)
          2^29727+20273 is Fermat and Lucas PRP! (12.4107s+0.0008s)



          Interesting.

          What dominion does 31838235*2^29717+1 have over 1*2^29727+20273?

          Is 80 days the best that can be done for the top primo prime?


          http://primes.utm.edu/primes/page.php?id=89447



          pfgw still ROCKS!


          Cino




          To: primenumbers@yahoogroups.com
          From: d.broadhurst@...
          Date: Tue, 1 Sep 2009 22:24:24 +0000
          Subject: [PrimeNumbers] Re: Some Benchmark Primality Test





          --- In primenumbers@yahoogroups.com,
          cino hilliard <hillcino368@...> wrote:

          > 31838235*2^29717+1 is prime! (15.3991s+0.0311s)

          OK

          > This 8954 digit number will be the top primo candidate
          > if you have the time

          Using ECPP to re-prove a prime already proven by BLS
          would be an exercise in fatuity.

          David










          [Non-text portions of this message have been removed]
        • djbroadhurst
          ... Very roughly, I reckon that the Primo time is proportional to digits^(9/2). David
          Message 4 of 5 , Sep 1, 2009
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            --- In primenumbers@yahoogroups.com,
            cino hilliard <hillcino368@...> wrote:

            > At first, I thought time was proportional
            > to the number of digits but now I realize
            > that ain't so.

            Very roughly, I reckon that the Primo time is proportional to digits^(9/2).

            David
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