Small gaps between products of two primes

  title={Small gaps between products of two primes},
  author={Sean W Graham and J. PINTZ and C. Y. Yildirim},
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) νeν−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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