Some problems on primitive roots and divisors in number theory.

Question

I have two questions:

1. Let $n>1$ be a positive integer that isn't a perfect power. Is $n$ a generator mod infinitely many primes?

2. Let $C,x,y$ be pairwise coprime integers $\in \mathbb{N}$. Let $a_n=Cx^n-y$. For all primes $p> cxy$, must there exist a divisor $d\mid a_i$ for some $i$ and $d$ is a primitive root mod $p$

They look like advanced problems and size theorems like Kobayashi or Zsigmondy don't seem to work. For p2, I'm trying to show that the divisors of $Cx^n-y$ can form a complete nonzero residue set mod $p$, but I seem to have reached a dead end.

UPD: 1 is Artin's conjecture, but 2 is probably solvable.