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arXiv · 2511.05631

The exceptional set of Goldbach problem and Linnik's constant

Genheng Zhao
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Abstract

Let $E(X)$ denote the number of even integers below $X$ which are not a sum of two primes. We prove the bound $E(X)=O(X^{\frac{7}{10}})$, where the implicit constant is ineffective. The method applied here also leads to $P(q)=O(q^5)$, where $P(q)$ denotes the least prime, if it exists, in any arithmetic progression modulo $q$.

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Genheng Zhao. 2025-11-07. The exceptional set of Goldbach problem and Linnik's constant. https://arxiv.org/abs/2511.05631

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