A promising approach to the twin prime problem

Abstract

The famous twin prime conjecture asserts that there are infinitely many pairs of primes differing by 2. More generally, it is conjectured that for any even number h, there are infinitely many pairs of primes differing by h. (This is obviously false for odd h.) Indeed, in a famous paper, G H Hardy and J E Littlewood made the following (much stronger) conjecture.