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Re: NO absolute-perfect cuboid exists

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  • David Broadhurst
    ... leavemsg1 wrote ... just in time for All Fools Day. More seriously, I remark that one is unlikely to be found. Heuristically the
    Message 1 of 2 , Mar 31, 2009
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      --- In primenumbers@yahoogroups.com,
      "leavemsg1" <leavemsg1@...> wrote

      > Date: Wed Apr 1, 2009 12:04 am
      > i. an absolute-perfect cuboid cannot exist

      just in time for All Fools' Day.

      More seriously, I remark that one is unlikely to be found.
      Heuristically the probability of finding a primitive
      perfect brick, all of whose sides are greater than x,
      is less than 1/x^(3/2).

      Bill Butler's Skulltrail found none with odd side < 10^11:
      http://www.durangobill.com/IntegerBrick.html

      So don't bet on one being one found real soon;
      they are conjecturally not Zariski dense:
      http://www.math.leidenuniv.nl/~rvl/ps/cuboids.ps

      David
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