My uncle's factorization algorithms
This is very interesting. Thank you for devoting your time to putting this on the web. Otherwise it might have rotted in your attic!<p>It's unclear to me whether there is anything theoretically new in here yet. The algorithms are all familiar to me except for the  P^2 + 1 and P^2 + P + 1 algorithms. But don't read too much into that. They are probably well known.<p>What I can tell you is that there is an extraordinary amount of work in implementing all those algorithms. I do this stuff for a living and it is a tremendously impressive feat for a single individual over any span of time.<p>I'd be interested in hearing how fast the MPQS is. The state of the art for factoring a number like 840931001586212064794450601167289569811131781103613687750579 on a single core is probably around 6s or so on a modern 2GHz x86 processor.<p>UBASIC already had a 32 bit x86 assembly optimised MPQS in it, and it performed pretty well actually. So it would be interesting if your uncle improved on that, especially if he had theoretical improvements.<p>The state of the art for the number field sieve should factor the 79 digit number here: <a href="http://www.loria.fr/~zimmerma/records/rsa.html" rel="nofollow">http://www.loria.fr/~zimmerma/records/rsa.html</a> in around 10-20 minutes on a single core, though in general the GNFS is for much larger integers. It seems unlikely that a little UBASIC program could manage those, however.<p>Having said that, I am still in shock that your uncle actually implemented the GNFS. That is a staggering accomplishment and is something to be genuinely impressed by.<p>I don't know if you have a gold mine there or the cutting edge life's work of someone from yesteryear.