DW> I agree that the process of analyzing this problem
 DW> has been very interesting. At the beginning of this
 DW> thread, someone (? Mark)

yup...

 DW> mentioned that it used to take a whole day to find
 DW> the first 100 triples.

that was on an IBM 4.77mhz PC, too... i wrote the program on a word
processor and then keyed it in in Turbo Pascal v3.0... it was very brute
force with three loops running and stepping thru every number... as simple
and brutish as one could get... most of the code was in the storage of the
results in a linked list in memory that was written to disk afterwards...

 DW> But, if people back then had thought about the problem
 DW> as thoroughly as we have done, I'm sure they could have
 DW> found 100 triples in an hour or two, using only
 DW> pencil-and-paper calculations. The vastly faster speeds
 DW> that we can achieve now are only partly the result of
 DW> much better calculating technology. Another major factor
 DW> is that we have immensely more efficient algorithms than
 DW> the trial-and-error method that is the most obvious one
 DW> to try. The latest version of the program is thousands
 DW> of times faster than my first attempt, which was
 DW> basically a hunt-and-peck effort.
 DW>
 DW> Good computers are useful. But they are no substitute for
 DW> clear thought.

you are correct... i'm toying with the idea of translating you last to
pascal and seeing how it compares ;)

)\/(ark