This isn't actually the Sieve of Eratosthenes. My undergrad advisor published a short piece about a family of functional prime generators of this form, that don't have nearly the efficiency of the true Sieve: http://www.cs.hmc.edu/~oneill/papers/Sieve-JFP.pdf

The gist of the problem is this: in the true sieve, each number is touched once for each of its prime factors. In this sieve, each number is touched once by each prime smaller than it (until a factor is found.)

There are a lot more primes that aren't factors of a given number than primes that are.