Uniform Bounds for the Least Almost-Prime Primitive Root

Abstract

We investigate, using the weighted linear sieve, the distribution of almost-primes among the residue classes (mod p) that generate the multiplicative group of reduced residue classes. We are concerned with finding an upper bound for the least prime or almost-prime primitive root (mod p) that holds uniformly for all p, analogous to Linnik's Theorem on a uniform upper bound for the least prime in a single arithmetic progression (mod p).