Some remarks on the first Hardy-Littlewood conjecture

2019/04/04 by Marco Bortolomasi, Bortolomasi, Marco, Arturo Ortíz-Tapia +1
Mathematics · #11Z05 #Analytic Number Theory Research #FOS: Mathematics #History and Overview (math.HO) #Limits and Structures in Graph Theory #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1904.03017

openalex publication_date 2019/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Starting from the first Hardy-Littlewood conjecture some topics will be covered: an empirical approach to the distribution of the twin primes in classes mod(10) and a simplified proof of the Bruns theorem . Finally, it will be explored an approach based on numerical analysis: Monte Carlo Method and Low discrepancy Sequences will be used to prove the convergence of the conjecture to the expected values.

Citations

• Characterization of the Distribution of Twin Primes

Related

• Contradictions in some primes conjectures
• The Hardy-Littlewood conjectures on the twin primes and the binary Goldbach problem are true
• Characterization of the Distribution of Twin Primes
• Asymptotic of the greatest distance between adjacent primes and the Hardy-Littlewood conjecture
• Some Results on a Conjecture of Hardy and Littlewood