Although the "Proof Attempts" section is interesting. It says that Artin's conjecture is true for all primes except possibly at most two exceptional primes p. It's not clear to me whether this is the weak conjecture (p is a primitive root for an infinite number of moduli) or the strong conjecture (p is a primitive root for Artin's conjectured proportion of moduli). On 1/31/2012 7:53 PM, Dan Asimov wrote:
The absence of concrete results on Artin's conjecture is amazing.
According to Wikipedia there is not even one integer N for which it is known that N is a primitive root modulo p for infinitely many primes p. Not even N = 2. Amazing.
--Dan
<< And that is devastating because (pathetically!) it is not even known that 10 is a prim-root modulo more than a finite set of primes: http://en.wikipedia.org/wiki/Artin's_conjecture_on_primitive_roots