Small gaps between primes or almost primes

D. A. Goldston, S. W. Graham, J. Pintz +1

Let $p_n$ denote the $n^{th}$ prime. Goldston, Pintz, and Yildirim recently proved that ${\mathrm{liminf}}_{n\to \infty }\frac{(p_{n+1}-p_n)}{\log p_n}=0.$ We give an alternative proof of…