I wonder if I have found something new which is, that the number of primitive triples from 3,4,5 up to Hypotenuse N, is close to 16% of N. +/-3. (Up to N = 2000 in my trials) N falls below this when N has only one prime factor of form 4n+1, and rises when it has more than one (different) prime factor, since the number of triples with a particular Hypotenuse = 2^(p-1) where p = the number of different prime factors of form 4n+1