-> Right ... I must admit I've been relishing the analysis-and-prune  
-> process rather than the absolute speed;  I get a feeling that  
-> seeking absolute speed will corrupt most `rational' processes from  
-> any explanatory role achieved.. 
  
I agree that the process of analyzing this problem has been very 
interesting. At the beginning of this thread, someone (? Mark) 
mentioned that it used to take a whole day to find the first 100 
triples. But, if people back then had thought about the problem as 
thoroughly as we have done, I'm sure they could have found 100 triples 
in an hour or two, using only pencil-and-paper calculations. The vastly 
faster speeds that we can achieve now are only partly the result of 
much better calculating technology. Another major factor is that we 
have immensely more efficient algorithms than the trial-and-error 
method that is the most obvious one to try. The latest version of the 
program is thousands of times faster than my first attempt, which was 
basically a hunt-and-peck effort. 
  
Good computers are useful. But they are no substitute for clear 
thought. 
  
                             dow 
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