When you use primes for your modulo, you get unique representation. This is a result of the Chinese remainder theorem. If my key is k, then calculating

    k mod 2
    k mod 3
    k mod 5
    ...
    k mod 29

uniquely determines k mod 2* 3* ...* 29. This way there are no collisions. Any set of pairwise relatively prime moduli would work, but using using primes is simple and it's easy to extend (just add the next prime to the list moduli).