As a separate note, I'm really disinclined to accept Monte Carlo proofs in the hard sciences.

I guess that means you don't trust public key encryption then, because RSA needs prime numbers to work with, but everybody just uses a variation of the Fermat test to check whether the keys generated are probably prime. But most people aren't overly concerned by this because you can set your threshold for "probably" to be, say, 100 times lower than the probablity that cosmic radiation will flip a bit in your memory causing an otherwise perfect algorthim to fail.