On sums of finite subsets of the primes

2025/03/05 by Zhao, Genheng
Mathematics · #Analytic Number Theory Research #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2503.03402

Abstract

Let A⊂ [1,x] be a non-empty set of primes with |A|= αx(log x)^-1. We prove that there exist absolute constants c₁,c₂>0 such that, as x gets sufficiently large, we have |A+A|≥ c₁(log x)(log log 3α^-1)^-1|A| if α≥ c₂(log x)^-1/2log log x and otherwise |A+A|≥ c₁(log x) (log 2α^-1)^-1|A|.

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