Miles Parker wrote:

And correct me if I'm wrong, but there are some algorithms in which using a prime number would be a bad idea. Anyway, it seems to me that any decent random stream generator should be able to take an arbitrary seed and produce a good result.

Primes etc. are really a figment of early linear congruential generators, for which non-prime parameters in the generator itself were famously bad choices (actually, not just non-prime but non-relatively-prime).  Knuth III is very interesting in that regard.