A Short Note on Gaps between Powers of Consecutive Primes

2017/09/22 by David Lowry-Duda, Lowry-Duda, David
Mathematics · #Advanced Mathematical Theories #Analytic Number Theory Research #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1709.07847

openalex publication_date 2017/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let α, β≥ 0 and α+ β< 1. In this short note, we show that \liminf_{n → ∞} p_n^β(p_n+1^α- p_n^α) = 0, where p_n is the nth prime. This notes an improvement over results of Sándor and gives additional evidence towards a conjecture of Andrica. This follows directly from recent results on prime pairs from Maynard, Tao, Zhang.

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