@article{Goldston2005SMALLGB,
title={SMALL GAPS BETWEEN PRIMES OR ALMOST PRIMES},
author={D. Goldston and S. Graham and J. Pintz and C. Y. Yilidirm},
journal={Transactions of the American Mathematical Society},
year={2005},
volume={361},
pages={5285-5330}
}

Let p n denote the n th prime. Goldston, Pintz, and Yildirim recently proved that li m in f (pn+1 ― p n ) n→∞ log p n = 0. We give an alternative proof of this result. We also prove some corresponding results for numbers with two prime factors. Let q n denote the n th number that is a product of exactly two distinct primes. We prove that lim inf(qn+1―q n ) n→∞ 26. If an appropriate generalization of the Elliott-Halberstam Conjecture is true, then the above bound can be improved to 6.