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16055[PrimeNumbers] Re: Sieving primo-factorials

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  • Jens Kruse Andersen
    Feb 9, 2005
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      I wrote:
      > > The default trial factor depth in pfgw -f tries to be near optimal, i.e.
      > > stop when the "expected" factoring time matches prp time (although
      > > different prp times for different forms is not taken into account).

      D├ęcio wrote:
      > Except that it doesn't take into account the fact that n! +/- n# +/- 1 isn't
      > divisible by primes up to n; Jim suggested that I try -f35 instead of the
      > default, as that's near optimal according to his experiments.

      Avoiding divisibility by small primes is irrelevant for the trial factor
      limit. After n is passed, every prime p has estimated chance 1/p of being a
      factor in a sufficiently "random" form without special factor properties.

      The default -f is much better than no factoring, but experimentation can
      sometimes find a better limit.
      A lot of things play in so it is hard for pfgw to guess the best limit when it
      doesn't first time a partial factoring and prp'ing of the particular number
      (and pfgw shouldn't start doing that).
      I wrote "different prp times for different forms is not taken into account".
      This is one thing pfgw could do but it requires analyzing the form before

      > I should grab that version -- I was running the latest compiled binary for
      > Linux that was available in the files area of the openpfgw group.

      Note that development versions at openpfgw are often less tested than released
      versions at primeform group.
      Factors can be trivially verified so a possibility is:
      Factor with development, verify factors, prp with release.

      Jens Kruse Andersen
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