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arXiv · 2503.03402

On sums of finite subsets of the primes

Genheng Zhao
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Abstract

Let $A\subset [1,x]$ be a non-empty set of primes with $|A|= αx(\log x)^{-1}$. We prove that there exist absolute constants $c_1,c_2>0$ such that, as $x$ gets sufficiently large, we have $|A+A|\geq c_1(\log x)(\log \log 3α^{-1})^{-1}|A|$ if $α\geq c_2(\log x)^{-1/2}\log \log x$ and otherwise $|A+A|\geq c_1(\log x) (\log 2α^{-1})^{-1}|A|$.

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Genheng Zhao. 2025-04-15. On sums of finite subsets of the primes. https://arxiv.org/abs/2503.03402

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