## Yıldırım, Small gaps between primes or almost primes

by
D. A. Goldston
,
S. W. Graham
,
J. Pintz
,
C. Y. Yildirim

Citations: | 8 - 2 self |

### BibTeX

@MISC{Goldston_yıldırım,small,

author = {D. A. Goldston and S. W. Graham and J. Pintz and C. Y. Yildirim},

title = {Yıldırım, Small gaps between primes or almost primes},

year = {}

}

### OpenURL

### Abstract

Abstract. Let pn denote the nth prime. Goldston, Pintz, and Yıldırım recently proved that (pn+1 − pn) lim inf =0. n→ ∞ log pn 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. 1.