  As a refinement of the celebrated recent work of Yitang Zhang we show that
any admissible k-tuple of integers contains at least two primes and almost
primes in each component infinitely often if k is at least 181000. This implies
that there are infinitely many gaps between consecutive primes of size at most
2530338, with an improved admissible k-tuple of Andrew W. Sutherland to
2326476.
