Primes in Sumsets

Abstract

We obtain an upper bound for the number of pairs $(a,b)\in A\times B$ such that $a+b$ is a prime number, where $A,B\subseteq \{1,...,N\}$ 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.

12 pages, Accepted in Archiv der Mathematik