Shors algorithm for factoring in polynomial time on a quantum computer gives an enormous advantage over all known classical factoring algorithm. We demonstrate how to factor products of large prime numbers using a compiled version of Shors quantum factoring algorithm. Our technique can factor all products of p, q such that p, q are unequal primes greater than two, runs in constant time, and requires only two coherent qubits. This illustrates that the correct measure of difficulty when implementing Shors algorithm is not the size of number factored, but the length of the period found.