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Re: LLRP4 Version 3.3 now available !

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  • Jean PennĂ©
    Thank you for your tests ! I am not surprised if LLPP4 deterministic test is slower than pfgw PRP one, because the Computing U0 loop is more time consuming
    Message 1 of 6 , Dec 1, 2004
      Thank you for your tests !

      I am not surprised if LLPP4 deterministic test is slower than pfgw PRP
      one, because the "Computing U0" loop is more time consuming than the
      LL loop... Is the deterministic pfgw test also faster ?

      Second question : with composite candidates, you found different
      residues with pfgw and with LLRP4, it may be normal, or it may be
      still an LLR bug...

      Regards,

      Jean


      --- In primenumbers@yahoogroups.com, "pminovic" <pminovic@y...> wrote:
      >
      > Jean,
      > Thank you for the new version in almost no time!
      >
      > I tried to test Kynea numbers. It's working but it's slower
      > than pfgw. Two examples are given below. Now I'm testing k*2^n+1.
      >
      > (2^110614+1)*2^110616-1 = (2^110615+1)^2 - 2 is prime! Time :
      > 929.038 sec. [LLR 3.3, 2.4 GHz P4]
      >
      > (2^110615+1)^2-2 is 3-PRP! (767.4431s+0.0228s) [pfgw, 2.2 GHz P4]
      >
      > --------------------
      > (2^240067+1)*2^240069-1 = (2^240068+1)^2 - 2 is not prime. Res64:
      > A06A1D3A94955672 Time : 4842.764 sec. [LLR-3.3, 2.4GHz P4]
      >
      > (2^240065+1)^2-2 is composite: [1FA6F8AA16DC1765] (3412.6447s+0.0320s)
      > [pfgw, 2.4GHz P4]
      >
      > Regards,
      > Predrag
    • pminovic
      ... PRP ... This is true, it takes about 50 minutes to compute U0, I ll append the lresults.txt file tomorrow. ... No! To prove primality of a PRP using pfgw
      Message 2 of 6 , Dec 1, 2004
        > I am not surprised if LLPP4 deterministic test is slower than pfgw
        PRP
        > one, because the "Computing U0" loop is more time consuming than the
        > LL loop...

        This is true, it takes about 50 minutes to compute U0, I'll
        append the lresults.txt file tomorrow.

        > Is the deterministic pfgw test also faster ?

        No! To prove primality of a PRP using "pfgw -tp" is very slow.
        Again I don't have exact timings handy but I think at least an
        hour in comparison to less than 18 minutes to find that
        (2^110615+1)^2-2 is 3-PRP.

        > Second question : with composite candidates, you found different
        > residues with pfgw and with LLRP4, it may be normal, or it may be
        > still an LLR bug...

        The input is different too, n=240068 and n=240065. The survival
        rate of Kynea (and Carol) is high and there are so many
        candidates to test that I simply cannot afford to process the
        same number twice :-)) Will try the same number later using
        smaller exponents.

        BTW, testing k*2^n+1, n~180,000, both the new LLR and PRP3
        could process one number in almost exactly the same time, about
        66 sec on 2.4GHz P-4.

        Regards,
        Predrag
      • Ken Davis
        The following is posted on behalf of Jean Penne who sent his reply to primenumbers-owner instead of primenumbers by mistake. Cheers Ken ... pfgw ... the
        Message 3 of 6 , Dec 1, 2004
          The following is posted on behalf of "Jean Penne" who sent his reply
          to "primenumbers-owner" instead of "primenumbers" by mistake.
          Cheers
          Ken
          --- In primenumbers@yahoogroups.com, "pminovic" <pminovic@y...>
          wrote:
          >
          > > I am not surprised if LLPP4 deterministic test is slower than
          pfgw
          > PRP
          > > one, because the "Computing U0" loop is more time consuming than
          the
          > > LL loop...
          >
          > This is true, it takes about 50 minutes to compute U0, I'll
          > append the lresults.txt file tomorrow.
          >

          Thanks by advance !

          > > Is the deterministic pfgw test also faster ?
          >
          > No! To prove primality of a PRP using "pfgw -tp" is very slow.
          > Again I don't have exact timings handy but I think at least an
          > hour in comparison to less than 18 minutes to find that
          > (2^110615+1)^2-2 is 3-PRP.
          >

          I am also not surprised : Deterministic pfgw pays for its more
          general algorithms than those of LLR.

          > > Second question : with composite candidates, you found different
          > > residues with pfgw and with LLRP4, it may be normal, or it may be
          > > still an LLR bug...
          >
          > The input is different too, n=240068 and n=240065. The survival
          > rate of Kynea (and Carol) is high and there are so many
          > candidates to test that I simply cannot afford to process the
          > same number twice :-)) Will try the same number later using
          > smaller exponents.
          >

          My fault ! I did'nt see the inputs were different...

          > BTW, testing k*2^n+1, n~180,000, both the new LLR and PRP3
          > could process one number in almost exactly the same time, about
          > 66 sec on 2.4GHz P-4.
          >

          Again, I am not surprised, PRP3 and LLRP4 use exactly the same code
          to do squarings, the only difference is that, for Proth deterministic
          tests, LLR computes the base "a" for each number, although PRP3 sets
          always "a" = 3, but all that is done outside the loops.

          Regards,
          Jean
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