Proof of Legendre's Conjecture

2012/11/26 by Ankush Goswami, Goswami, Ankush
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1211.6046

Some errors to be fixed

openalex publication_date 2012/11/26 · arxiv created 2012/11/28 · arxiv updated 2012/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Legendre's conjecture states that there exists a prime between n² and (n+1)², for every positive integer n. Here I prove that for sufficiently large n, there is a prime number between n² and (n+1)². The proof relies on the idea of counting the maximum power, o_p(n) of a prime p≤ n such that p^o_p(n)||n.

Related

• Towards Proving Legendre's Conjecture
• Legendre's conjecture. Theorem on existence of a prime number between m² and (m+1)²
• On Legendre's, Brocard's, Andrica's, and Oppermann's Conjectures
• Legendre Conjecture over Arithmetic Progressions
• Weakening the Legendre Conjecture