On sums of sparse prime subsets

Abstract

For arbitrary c0 > 0, if A is a subset of the primes less than x with cardinality δx(log x) −1 with δ ≥ (log x) −c 0 , then there exists a positive constant c such that the cardinality of A + A is larger than c δx(log log x) −1 .

Goldbach Numbers in Short Intervals -- A Nonnegative Model Approach

“…Together with a minor arc estimate, this was used by Cui, Li, and Xue [CLX13] to give a lower bound to sums of sparse subsets of the primes. So we could choose T + ν (n) as a scaled rough number indicator and generalize [CLX13] into short intervals, as required for (9).…”