Primes in sumsets

We obtain an upper bound for the number of pairs ( (a,b) in {Atimes B} ) such that ( a+b ) is a prime number, where ( A, B subseteq {1,ldots ,N }) with (|A||B| , gg frac{N^2}{(log {N})^2}), (, N ge 1) an integer. This improves on a bound given by Balog, Rivat, and Sárközy.