  We generalise Zhang's and Pintz recent results on bounded prime gaps to give
a lower bound for the the number of prime pairs bounded by 6*10^7 in the short
interval $[x,x+x (\log x)^{-A}]$. Our result follows only by analysing Zhang's
proof of Theorem 1, but we also explain how a sharper variant of Zhang's
Theorem 2 would imply the same result for shorter intervals.
