A note on the geometric mean of prime numbers and generalizations. (4th July 2022) - Farhadian, Reza; Jakimczuk, Rafael
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.