Bounded Gaps Between Products of Distinct Primes
  Let $r \ge 2$ be an integer. We adapt the Maynard-Tao sieve to produce the asymptotically best-known bounded gaps between products of $r$ distinct primes. Our result applies to positive-density subsets of the primes that satisfy certain equidistribution conditions. This improves on the work of Thorne and Sono. 
Yang P. Liu, Peter S. Park, Zhuo Qun Song
math.NT