What's the benefit of seeding a random number generator with only prime numbers?

Question

While conducting some experiments in Java, my project supervisor reminded me to seed each iteration of the experiment with a different number. He also mentioned that I should use prime numbers for the seed values. This got me thinking — why primes? Why not any other number as the seed? Also, why must the prime number be sufficiently big? Any ideas? I would've asked him this myself, but its 4am here right now, everyone's asleep, I just remembered this question and I'm burning to know the answer (I'm sure you know the feeling).

It would be nice if you could provide some references, I'm very interested in the math/concept behind all this!

EDIT:

I'm using java.util.Random.

FURTHER EDIT:

My professor comes from a C background, but I'm using Java. Don't know if that helps. It appears that using primes is his idiosyncrasy, but I think we've unearthed some interesting answers about generating random numbers. Thanks to everyone for the effort!

Answer 1

Well one blink at the implementation would show you that he CAN'T have any reason for that claim at all. Why? Because that's how the set seed function looks like:

synchronized public void setSeed(long seed) {     seed = (seed ^ multiplier) & mask;     this.seed.set(seed);     haveNextNextGaussian = false; } 

And that's exactly what's called from the constructor. So even if you give it a prime, it won't use it anyhow, so if at all you'd have to use a seed s where (s^ multiplier) & mask results in a prime ;)

Java uses a usual linear congruency method, i.e.:

x_n+1 = (a * x_n + c) mod m with 2 <= a < m; 0 <= c < m.

Since you want to get a maximal periode, c and m have to be relatively prime and a few other quite obscure limitations, plus a few tips how to get a practically useful version. Knuth obviously covers that in detail in part2 ;)

But anyhow, the seed doesn't influence the qualities of the generator at all. Even if the implementation would be using a Lehmer generator, it would obviously make sure that N is prime (otherwise the algorithm is practically useless; and not uniformly distributed if all random values would have to be coprime to a non prime N I wager) which makes the point moot

Answer 2

If the generator is a Lehmer generator, than the seed and the modulus must be co-prime; see the wiki page. One way to ensure they are co-prime is to start with a prime number.