Small gaps between products of two primes - Goldston, D. A.; Graham, S. W.; Pintz, J.; Y ld r m, C. Y. (Proceedings of the London Mathematical Society, 2009)
Let qn denote the nth number that is a product of exactly two distinct primes. We prove that qn+1 − qn ≤ 6 infinitely often. This sharpens an earlier result of the authors, which had 26 in place of 6. More generally, we prove that if ν is any positive integer, then (qn+ν − qn) ≤ ν eν − γ (1+o(1)) infinitely often. We also prove several other related results on the representation of numbers with exactly two prime factors by linear forms.