On the moments of the gaps between consecutive primes

2017/05/30 by Marek Wolf, Wolf, Marek
Mathematics · #11N35 #11P32 #11Y55 #Analytic Number Theory Research #Combinatorics #FOS: Mathematics #Geometry #History and Theory of Mathematics #Mathematics #Mathematics and Applications #Number Theory (math.NT) #Physics #Pi #Primary 11A41 #Secondary 11N05 #math.NT #msc:11A41 #msc:11N05 #msc:11N35 #msc:11P32 #msc:11Y55

paper · pdf · doi:10.48550/arxiv.1705.10766

published in arXiv (Cornell University) (Cornell University)

arxiv created 2017/05/30 · openalex publication_date 2017/05/30 · arxiv updated 2017/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive heuristically formula for the k--moments M_k(x) of the gaps between consecutive primes

Citations

• Some heuristics on the gaps between consecutive primes
• Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4⋅10¹⁸
• Some problems of ‘Partitio numerorum’; III: On the expression of a number as a sum of primes

Related

• Negative moments of the gaps between consecutive primes
• Small Gaps Between Primes I
• Some heuristics on the gaps between consecutive primes
• Primes in Tuples IV: Density of small gaps between consecutive primes
• On the ratio of consecutive gaps between primes