A heuristic study of the distribution of primes in short and not-so-short intervals

2018/04/20 by Miguel-Angel Sanchis-Lozano, Sanchis-Lozano, Miguel-Angel
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1804.07659

openalex publication_date 2018/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A numerical study on the distributions of primes in short intervals of length h over the natural numbers N is presented. Based on Cramér's model in Number Theory, we obtain a heuristic expression applicable when h ≫ logN but h ≪ N, providing support to the Montgomery and Soundararajan conjecture on the variance of the prime distribution at this scale.

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