Some conditional results on primes between consecutive squares

2011/12/01 by Danilo Bazzanella
Mathematics · #Analytic Number Theory Research #Limits and Structures in Graph Theory #Algebraic Geometry and Number Theory

paper · pdf · doi:10.7169/facm/1323705816

Abstract

A well-known conjecture about the distribution of primes asserts that between two consecutive squares there is always at least one prime number. The proof of this conjecture is quite out of reach at present, even under the assumption of the Riemann Hypothesis. The aim of this paper is to provide the upper bounds for the exceptional set for this conjecture under the assumption of some heuristic hypotheses.

Citations

• Primes between consecutive squares

Related

• Existence of primes between two consecutive squares
• Weakening the Legendre Conjecture
• Distribution of Large Gaps Between Primes
• Sums of Consecutive Prime Squares
• On solutions of some of unsolved problems in number theory, specifically on the distribution of primes