Density versions of the binary Goldbach problem

2024/05/28 by Ali Alsetri, Alsetri, Ali, Xuancheng Shao +1 · 2 citations
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2405.18576

openalex publication_date 2024/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let δ> 1/2. We prove that if A is a subset of the primes such that the relative density of A in every reduced residue class is at least δ, then almost all even integers can be written as the sum of two primes in A. The constant 1/2 in the statement is best possible. Moreover we give an example to show that for any ε > 0 there exists a subset of the primes with relative density at least 1 - ε such that A+A misses a positive proportion of even integers.

Cited by

• Problems 66 and 67 on sums of residue classes and primes of András Sárközy's collection of unsolved problems
• Density ternary Goldbach for primes in a fixed residue class

Related

• Density ternary Goldbach for primes in a fixed residue class
• The ternary Goldbach problem with primes in positive density sets
• Sumsets in primes containing almost all even positive integers
• A density version of Waring-Goldbach problem
• The binary Goldbach conjecture is also true