The Cramér conjecture holds with a positive probability

2018/02/23 by Naser T. Sardari, Sardari, Naser T.
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1802.08524

openalex publication_date 2018/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a positive proportion of the intervals of any fixed scalar multiple of log(X) in the dyadic interval [X,2X] contain a prime number. We also show that a positive proportion of the congruence classes modulo q contain a prime number smaller than any fixed scalar multiple of φ(q)log(q).

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