2019/09/27 by Christian Axler, Axler, Christian
Mathematics · #11A99 (Secondary) #11N05 (Primary) #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematics and Applications #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1909.12625
openalex publication_date 2019/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let m and n be positive integers with m,n ≥ 2. The second Hardy-Littlewood conjecture states that the number of primes in the interval (m,m+n] is always less than or equal to the number of primes in the interval [2,n]. Based on new explicit estimates for the prime counting function π(x), we give some new ranges in which this conjecture holds.