A note on the geometric mean of prime numbers and generalizations. (4th July 2022)

• Record Type: Journal Article
• Authors: Farhadian, Reza; Jakimczuk, Rafael
• Is Part Of: Journal of discrete mathematical sciences & cryptography. Volume 25:Number 5(2022)
• Page Start: 1213
• Page End: 1223
• Publication Date: 2022-07-04
• Subjects: Primary: 11A41 -- Secondary: 11N05; Prime numbers -- Geometric mean -- Limit behavior; Computer science -- Mathematics -- Periodicals; Cryptography -- Periodicals; Computer science -- Mathematics; Cryptography; Periodicals; 004.0151
• DOI: 10.1080/09720529.2020.1723920
• Languages: English
• ISSNs: 0972-0529

Abstract

Abstract: Let pn denote the n -th prime number and let Gn be the geometric mean of the first n primes. It is well-known that Gn / pn → 1/ e as n → ∞, where e is the Euler's number. The aim of this note is to give various proofs of this fact, equivalent establishments and generalizations.