Hardy-Littlewood inequality for primes

2015/04/27 by V. V. Miasoyedov, Miasoyedov, V. V.
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematics and Applications #Number Theory (math.NT) #Primary 11N05 #secondary 11P32

paper · pdf · doi:10.48550/arxiv.1504.07939

openalex publication_date 2015/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the article we establish the Hardy-Littlewood inequality π(x + y) ≤ π(x) + π(y) . We also prove that the naturally ordered primes p₁=2,p₂=3,p₃=5,p₄=7,… satisfy the inequality p_ a + b> p_a + p_b for all a, b ≥ 2.

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