Chen primes in arithmetic progressions

TL;DR

This paper establishes a uniform lower bound for the quantity of Chen primes within specific arithmetic progressions, extending understanding of their distribution under certain modular constraints.

Contribution

It provides a new uniform lower bound for Chen primes in arithmetic progressions with moduli up to a logarithmic power, advancing prime distribution theory.

Findings

Lower bound for Chen primes in arithmetic progressions

Uniform estimate valid for q up to log^M x

Enhanced understanding of Chen primes distribution

Abstract

We find a lower bound for the number of Chen primes in the arithmetic progression $a \bmod q$, where $(a,q)=(a+2,q)=1$. Our estimate is uniform for $q \leq \log^M x$, where $M>0$ is fixed.