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.
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页码：1213 / 1223
页数：11
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