The exceptional set of Goldbach problem and Linnik's constant

2025/11/07 by Zhao, Genheng
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2511.05631

openalex publication_date 2025/11/07 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/28

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^(7)/(10)), where the implicit constant is ineffective. The method applied here also leads to P(q)=O(q⁵), where P(q) denotes the least prime, if it exists, in any arithmetic progression modulo q.

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