Binary expansions of prime reciprocals

Abstract

Prime numbers have been always of great interest. In this work, we explore the prime numbers from a sieve other than the Eratosthenes sieve. Given a prime number $p$, we consider the binary expansion of $\frac{1}{p}$ and, in particular, the size of the period of $\frac{1}{p}$. We show some results that relate the size of the period to properties of the prime numbers.