Oh and now having looked up the sieve of Eratosthenes... that would work fine for problem 2, but I think it would be pretty difficult for problem 1. The trouble is that the sieve assumes that you have a specific largest integer in mind: for example, all the primes between 1 and 300. But for problem 1, we're trying to find our largest integer: the 1000th prime number.

You could probably kludge it by getting, say, every prime number between 1 and 10,000 and then hoping that the 1000th prime is in there. But that would be pretty inefficient.