A note on the geometric mean of prime numbers and generalizations

被引：0

作者：

Farhadian, Reza ^{[1
]}

Jakimczuk, Rafael ^{[2
]}

机构：

[1] Lorestan Univ, Dept Stat, Khorramabad, Iran

[2] Univ Nacl Lujan, Div Matemat, Buenos Aires, DF, Argentina

来源：

JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY | 2022年 / 25卷 / 05期

关键词：

Prime numbers; Geometric mean; Limit behavior;

D O I：

10.1080/09720529.2020.1723920

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let p(n) denote the n-th prime number and let G(n) be the geometric mean of the first n primes. It is well-known that G(n) /p(n) -> 1/e as n -> infinity, where e is the Euler's number. The aim of this note is to give various proofs of this fact, equivalent establishments and generalizations.

引用

页码：1213 / 1223

页数：11

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