On the set of the difference of primes

TL;DR

This paper proves that the set of differences between primes has a specific combinatorial property, leveraging recent breakthroughs in understanding bounded gaps between primes by Zhang, Maynard, and Tao.

Contribution

It establishes that the set of prime differences is a $\Delta_r^*$-set, connecting prime gap results with combinatorial set properties.

Findings

The set of prime differences is a $\Delta_r^*$-set.

The proof relies on recent advances in bounded prime gaps.

Connects prime gap theory with combinatorial set theory.

Abstract

In this work we prove that the set of the difference of primes is a $\Delta_r^*$-set. The work is based on the recent dramatic new developments in the study of bounded gaps between primes, reached by Zhang, Maynard and Tao.