Some Notes on the Distribution of Mersenne Primes

摘要

Mersenne primes are a special kind of primes, which are always an important content in number theory. The study of Mersenne primes becomes one of hot topics of the nowadays science. It has not settled that whether there exist infinite Mersenne primes. And several of conjectures on the distribution of it provided by scholars. Starting from the Mersenne primes known about, in this paper we study the distribution of Mersenne primes and argued against some suppositions by data analyzing.