If you have a strong RSA modulus, e.g. 2048 bits, then the primes we are talking about are about 1024 bits. There is no way you are going to hit such a prime n

If you have a strong RSA modulus, e.g. 2048 bits, then the primes we are talking about are about 1024 bits. There is no way you are going to hit such a prime number at random. Not even if you set a million fast computers going in a million universes on every planet in those universes. Certainly not before heat death of this universe. The only way you are going to have an interest in this prime is as a factor of someone's RSA key (for which you will need not-yet-invented algorithms of great sophistication and probably an enormous amount of computer time to find in the first place). On principle, the idea of illegal numbers is stupid. Actually, on second thoughts, it is stupid either way. It is basically serving only as a legal backstop for a situation that by definition shouldn't need one.