W Sequences and the Distribution of Primes in Short Interval

TL;DR

This paper introduces W Sequences, special sequences derived from Euclid's algorithm, which connect to prime distribution in short intervals and offer new perspectives on classical number theory problems.

Contribution

It presents the concept of W Sequences and explores their potential in understanding prime distribution and reformulating classical number theory problems.

Findings

W Sequences relate to prime distribution in short intervals

They enable weakened forms of classical number theory problems

Preliminary analysis suggests new research directions

Abstract

Based on Euclid's algorithm, we find a kind of special sequences which play an interesting role in the study of primes. We call them W Sequences. They not only ties up the distribution of primes in short interval but also enables us to give new weakened forms of many classical problems in Number Theory. The object of this paper is to provide a brief introduction and preliminary analysis on this kind of special sequences.