On sums of subsets of Chen primes

Abstract

In this paper we show that if $A$ is a subset of Chen primes with positive relative density $\hat{I}\pm$, then $A+A$ must have positive upper density at least $c\hat{I}\pm e^{-c^{\prime }\log (1/\hat{I}\pm {)}^{2/3}(\log \log (1/\hat{I}\pm ){)}^{1/3}}$ in the natural numbers.