Densities of Primes and Primitive Roots.

Let u ≠ ±1, v² be a fixed integer, let p be a prime number, and let ord_p(u) = d|p - 1 be the order of u mod p. This note provides a lower bound #{p ≤ x : ord_p(u) = p-1} ≫ x(log x)^-1 for the number of primes p ≤ x with a fixed primitive root u mod p for all large numbers x ≥ 1. The current results in the literature have the lower bound #{p ≤ x : ord_p(u) = p - 1} ≫ x(log x)^-2, and restrictions on the fixed primitive root to a subset of at least three or more integers. [ABSTRACT FROM AUTHOR]