Small gaps between products of two primes

@article{Goldston2009SmallGB,
  title={Small gaps between products of two primes},
  author={D. A. Goldston and Sidney W. Graham and Janos Pintz and C. Y. Yildirim},
  journal={Proceedings of the London Mathematical Society},
  year={2009},
  volume={98}
}
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. 
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