Incidentally, when I am talking about composite numbers as the difference between two squares, I am talking about what is generally known as "Fermat factorisation".
I should have mentioned or realised that sooner, but I am mostly working stuff out for fun here, and then occasionally trawling round to find proper mathematical accounts of the same subjects.
OK, I'm off to read a bit more about quadratic sieves etc as that may help me also.
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