Some Remarks on Artin's Conjecture

Source abstract

Abstract It is a classical conjecture of E. Artin that any integer a > 1 which is not a perfect square generates the co-prime residue classes (mod ρ) for infinitely many primes ρ. Let E be the set of a > 1, a not a perfect square, for which Artin's conjecture is false. Set E(x) = card( e ∊ E: e ≤ x ). We prove that E(x) = 0(log 6 x) and that the number of prime numbers in E is at most 6.