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Re: LLRP4 Version 3.3 now available !

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  • 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 1 of 6 , Dec 1, 2004
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      > 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 2 of 6 , Dec 1, 2004
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        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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