No I've never heard of busy beaver functions.. I'll have to look into them. Most of this stuff I learned during my various Discrete Mathematics courses here at UCF. I enjoyed the class about turing machines and noncomputability immensely. I think I will be taking a class in encryption soon.
KornNut- Yes, I have read Digital Fortress by Dan Brown, good book. Its interesting that you mention NP completeness, since that is also really interesting. If they could prove that prime number factorization was a problem that was in P, then thousands of other problems associated with it would be in P as well. Just imagine if they could prove the halting problem was in P!
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