On Thin Sets of Primes Expressible as Sumsets

Abstract

Suppose that P is an infinite set of primes such that P = A + B + C, where A,B,C are sets with at least two elements. We show that if P(x) > c x/log^d x (where P(x) = the number of elements of P that are <= x), and if A,B,C is a "regular" triple of sets, then either |A+B| <= d, or |B+C| <= d, or |A+C| <= d.