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Re: [PrimeNumbers] Residual Factorization Extension

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  • Alan Eliasen
    I ll have to admit that I even tried to implement Mr. Brown s algorithm, to torture-test the primality-checking routines in my programming language Frink ,
    Message 1 of 11 , Jan 4, 2004
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      I'll have to admit that I even tried to implement Mr. Brown's
      algorithm, to torture-test the primality-checking routines in my
      programming language "Frink", http://futureboy.homeip.net/frinkdocs/
      (although I'll certainly admit that the description given in his
      PowerPoint presentation does not give enough information to be usable to
      anyone. The mention of the "Nyquist Criterion" is, I believe,
      intentionally vague. I understand both the Nyquist stability criteria,
      and the Nyquist sampling criteria, and those who understand them will
      see, readily, that this mention is insufficient and inappropriate.)

      He also sent me a spreadsheet that just had unexplained numbers in
      it, all entered by hand; there was no equation in the entire thing, and
      was thus useless.

      In any case, even though the description was clearly insufficient, I
      gave him the benefit of the doubt and tried many different
      interpretations of the vague bits.

      For example, it's unclear what "minimums of R" means, so I tried all
      of the following:

      * Minimum value of R found in a range
      * Minimum absolute value of R
      * Minimum sum of values of R
      * Minimum sum of absolute values of R
      * Minimum RMS sum of values of R

      In addition, since this is obvious *incredibly* sensitive to the
      exact numbers you sample, I tried lots of sampling rates and sampling
      offsets, including very high sampling rates which should exceed any
      interpretation of the Nyquist sampling criterion, if indeed that is what
      was meant. I tried lots of "bin" sizes for the sums and averages. I
      also tried scaling the minima along with their magnitudes (the values of
      R tend to get larger as you sample larger numbers, of course.)

      I worked with numbers of which I knew the factors, and, to make a
      long story short, I see absolutely no evidence that the algorithm, as
      presented, has any utility. Even if you know the exact factors, and try
      really hard to make it fit, you can't even force the algorithm to point
      to the right places, other than what would be expected by pure
      probabilities. If you have 10 bins, 1/10 of the time you'll sample
      numbers that drop it in the right bin. I don't see that as strong evidence.

      Rather, it became quite clear that the minima found, even with the
      smoothing produced by summing, has a lot of stochastic variation which
      is directly due to the particular sample points that you chose.

      It is easy to see, therefore, that _post facto_, one could choose a
      set of sample points that "proved" this algorithm true if you already
      knew the factors of a number. I will absolutely not accept any post
      facto evidence as evidence that this algorithm works, especially when
      work is not shown.

      I agree that D├ęcio's test is fair, acceptable, and should well be
      within the reach of Mr. Brown's algorithm if it works as claimed. So,
      please, either provide the digits, or go back to the drawing board, and
      stop making further unsubstantiated claims. I would suggest that it is
      not a worthwhile use of one's time to attempt to reproduce this
      algorithm unless Mr. Brown provides the digits requested (unless you're
      writing a programming language that you're torture-testing. :) )

      If, indeed, he provides the factors, I will gladly help code the
      algorithms. Seems like pretty safe money.

      --
      Alan Eliasen | "You cannot reason a person out of a
      eliasen@... | position he did not reason himself
      http://futureboy.homeip.net/ | into in the first place."
      | --Jonathan Swift
    • Alan Eliasen
      Oh, and the fact that if you happen to sample dead-on a factor, that it doesn t produce a minimum, is exceptionally telling. -- Alan Eliasen |
      Message 2 of 11 , Jan 4, 2004
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        Oh, and the fact that if you happen to sample dead-on a factor, that
        it doesn't produce a minimum, is exceptionally telling.

        --
        Alan Eliasen | "You cannot reason a person out of a
        eliasen@... | position he did not reason himself
        http://futureboy.homeip.net/ | into in the first place."
        | --Jonathan Swift
      • grostoon
        Hi all and happy new year, I too have discovered an amazing algorithm that factorizes a composite integer N in O(log(log(Pmax))^1/2) where Pmax is the largest
        Message 3 of 11 , Jan 5, 2004
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          Hi all and happy new year,

          I too have discovered an amazing algorithm that factorizes a
          composite integer N in O(log(log(Pmax))^1/2) where Pmax is the
          largest prime factor of N !!!

          I have a truly marvelous demonstration of this proposition but this
          margin is too narrow to contain it...

          ;-)

          Jean-Louis.




          --- In primenumbers@yahoogroups.com, "Milton Brown" <miltbrown@e...>
          wrote:
          > Happy New Year to All:
          >
          > Based on my Residual Factorization Method described in
          >
          > www.csulb.edu/~mbrown10
          >
          > I can computer the first digits of RSA factors.
          >
          > I would like to obtain a program like ECM which will use these
          > digits to complete the factorization.
          >
          > Does anyone have such a program?
          >
          > Thanks,
          >
          > Milton L. Brown
          > miltbrown@e...
          >
          >
          >
          > [Non-text portions of this message have been removed]
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