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arXiv · 2605.14369

A density version of quaternary Goldbach problem

Xiaoyang Hu·Meng Gao
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Abstract

Let $\mathcal{P}$ denote the set of all primes, and let $\underline\delta(P)$ denote the relative lower density of a subset $P$ in $\mathcal{P}$. Suppose that $P_1, P_2, P_3, P_4$ are four subsets of primes with $\underline\delta(P_1)+\underline\delta(P_2)>1$ and $ \underline\delta(P_3)+\underline\delta(P_4)>1.$ Then for every sufficiently large even integer $n$, there exist primes $p_i \in P_i$ $(i=1,2,3,4)$ such that $n=p_1+p_2+p_3+p_4$. The condition is the best possible.

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Xiaoyang Hu, Meng Gao. 2026-05-14. A density version of quaternary Goldbach problem. https://arxiv.org/abs/2605.14369

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