Construction of normal numbers by classified prime divisors of integers

Abstract

Given an integer $d\ge 2$, a $d$-{\it normal number}, or simply a {\it normal number}, is a real number whose $d$-ary expansion is such that any preassigned sequence, of length $k\ge 1$, of base $d$ digits from this expansion, occurs at the expected frequency, namely $1/d^k$. We construct large families of normal numbers using classified prime divisors of integers.