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Re: [PrimeNumbers] Re: Yet another factoring puzzle

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  • Phil Carmody
    ... But is that more or less remarkable than the expectation of any one of Phil Taylor s darts landing in the region around where it actually landed? You only
    Message 1 of 23 , Sep 25, 2013
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      On Mon, 9/16/13, djbroadhurst wrote:
      --- "djbroadhurst" <d.broadhurst@...> wrote:
      > > Exercise 6: Find the complete factorization of F(n) for at
      > > least one even integer n > 600.
      > As far as I can tell, no-one (apart from the setter)
      > yet solved Exercise 6, which can be done in less
      > than 2 minutes, using OpenPFGW. What is remarkable
      > about this exercise is that it can be solved so
      > quickly. Heuristically, that was not to be expected.

      But is that more or less remarkable than the expectation of
      any one of Phil Taylor's darts landing in the region around
      where it actually landed? You only chose that target after
      the arrow had landed, I'm sure.

      How many mathematical diversions have you looked at
      via the medium of numerical computation? How many of
      them would you expect to be remarkably easier than
      expected to solve? Probably a non-zero answer. Don't
      be surprised that one particular example was one.

      Knowing what he's trying to say, even if he's not getting
      it across clearly,
      Phil
      --
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      [stolen with permission from Daniel B. Cristofani]
    • djbroadhurst
      ... It happened thus: 1) I determined to factorize F(n)=((n^2-9)/4)^2-5 for n
      Message 2 of 23 , Sep 27, 2013
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         ---In primenumbers@yahoogroups.com, <thefatphil@...> wrote:

         

        > You only chose that target after
        > the arrow had landed, I'm sure.

         

        It happened thus:

         

        1) I determined to factorize F(n)=((n^2-9)/4)^2-5 for
        n <= 300, completely. As later shown in "factordb", I succeeded.

         

        2) Meanwhile I ran OpenPFGW on n in [301,600], hoping for a
        quick outlier and found none.

         

        3) I estimated the probability of an easily discoverable
        completely factorization for n>600 and found it to be small.

         

        4) Recalling how I had once been caught out before by
        a "probably no more" heuristic, I set a lone process running on
        n in [601, 10000]  so as not to be caught out again by Jens.

         

        5) When I later looked  and pfgw.log, it had found a hit at
        n=608.

         

        So yes, Phil, you are quite correct that the puzzle was set
        after this finding. However the heuristic that I gave was
        made prior to my discovery, else I would not have said that
        I was surprised.

         

        The point that you are making (I think) is that I do such 
        expsriments often and only notice when the result is unexpected.
        I don't tell folk about all the boring times when a negative
        heuristic is borne out by a null result. That is the selection

        effect.

         

        David (guilty of not boring folk with what is routine)

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