Highly Influenced

# Small Gaps between Primes or Almost Primes

@inproceedings{Goldston2005SmallGB, title={Small Gaps between Primes or Almost Primes}, author={D. A. Goldston and Sean W Graham and Janos Pintz and C. Y. Yildirim}, year={2005} }

- Published 2005

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