Let ordp(a) be the order of a in (Z/pZ)∗. In 1927 Artin conjec- tured that the set of primes p for which an integer a ̸= −1, □ is a primitive root (i.e. ordp(a) = p − 1) has a positive asymptotic density among all primes. In 1967 Hooley proved this conjecture assuming the Generalized Riemann Hypothesis. In this talk we will study the behaviour of ordp(a) as p varies over primes, in particular we will show, under GRH, that the set of primes p for which ordp(a) is “k prime factors away” from p − 1 has a positive asymptotic density among all primes except for particular values of a and k. We will interpret being “k prime factors away” in three different ways, namely k = ω( p−1 ), k = Ω( p−1 ) and k = ω(p−1)−ω(ordp(a)), and present ordp (a) ordp (a) conditional results analogous to Hooley’s in all three cases and for all integer k. This is joint work with Leo Goldmakher and Greg Martin.