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Re: {Spam?} [PrimeNumbers] faster than the APR algorithm

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  • Paul Leyland
    ... Bunch of code omitted. ... Wish granted. Paul, hoping that you would comment on how it works instead of expecting us to decipher some turgid code which
    Message 1 of 33 , May 21, 2010
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      On Fri, 2010-05-21 at 15:28 +0000, leavemsg1 wrote:
      >
      > I believe that this algorithm proves primality faster than the
      > APR algorithm, not compositeness, but primality; if both this
      > T-sequence algorithm and the APR algorithm were written in the
      > same language and had the same FFT's and CPU available, then I
      > believe the T-sequence would beat it; assuming that variables
      > were computed on the fly... i.e. no stored values allowed.

      Bunch of code omitted.

      > Bill, hoping that someone would comment on it other than DjBrst

      Wish granted.

      Paul, hoping that you would comment on how it works instead of expecting
      us to decipher some turgid code which looks as if it was written in the
      early 1970s. Some kind of BASIC if my age-addled memory doesn't
      deceive me.
    • mikeoakes2
      ... You did very much what I did. I nearly fell off the chair when I averaged everything out and saw 0.57... :-) ... Not very. Would you buy an appeal to
      Message 33 of 33 , May 27, 2010
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        --- In primenumbers@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
        >
        > I tried 1/n^c:
        >
        > v=[1237.1, 328.7, 105.4, 28.01, 6.22 , 1.510, 0.439, 0.0939];
        > print(vector(8,k,-log(v[k]/10^6)/(k+4)/log(10)));
        >
        > [0.5815, 0.5805, 0.5682, 0.5691, 0.5785, 0.5821, 0.5780, 0.5856]
        >
        > and then A/n^c, using the first datum to remove A:
        >
        > print(vector(7,k,-log(v[k+1]/v[1])/k/log(10)));
        >
        > [0.5756, 0.5348, 0.5484, 0.5747, 0.5827, 0.5750, 0.5885]
        >
        > In both cases c =~ Euler looks rather convincing,
        > given the statistics. Well spotted, Sir!

        You did very much what I did.
        I nearly fell off the chair when I averaged everything out and saw 0.57... :-)

        > How strongly are you committed to A = 1, for the average,
        > given the variability of the overall factor with a?

        Not very.
        Would you buy an appeal to Occam's razor, mon vieux?

        Mike
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