Exploring Prime Gaps: Enhancing Zhang’s Breakthrough with Hyperdimensional Computing and Neuro-Symbolic AI

Preamble

Prime numbers have fascinated mathematicians for millennia, serving as the fundamental building blocks of number theory. Among the myriad of questions surrounding primes, the twin primes conjecture stands out as one of the most tantalizing and enduring mysteries.

In recent years, Yitang Zhang made headlines by making a groundbreaking advancement towards this conjecture. Building upon Zhang’s pioneering work, I have integrated Hyperdimensional Computing (HDC) and Neuro-Symbolic AI (NSAI) to further explore and explain prime gaps. This article dives into the intricacies of Zhang’s method, highlights my Vector Symbolic extensions, and showcases the profound implications of this hybrid approach.

Introduction

The distribution of prime numbers has been a central topic in number theory with implications spanning cryptography, computer science, and pure mathematics. Among the intriguing aspects of prime distribution are prime gaps — the differences between consecutive prime numbers. Understanding these gaps not only deepens our grasp of prime behavior but also propels forward our ability to predict and manipulate primes in various applications.