Existence of primes between two consecutive squares

TL;DR

This paper proves Legendre's Conjecture, asserting that there is always a prime between two consecutive perfect squares, addressing a long-standing open problem in number theory.

Contribution

The paper provides a proof of Legendre's Conjecture, establishing the existence of primes between consecutive squares, which was previously unproven.

Findings

Legendre's Conjecture is proven true.

There is always at least one prime between n^2 and (n+1)^2 for all natural n.

The result confirms a key hypothesis in number theory.

Abstract

Legendre's Conjecture is one of the most elegant open problems in Number Theory, which states that there is a prime between consecutive two perfect squares. In this note, we prove the conjecture holds true and also discuss the related results.