Existence of primitive roots Fix $p$ prime . Exist $q$ prime that p is primitive root $Z/qZ$ ?
I think that this is true (numerical evidence).

We need to put some conditions on $q$, such as $p\lt q$. This is because, for example, any odd prime $p$ is technically a primitive root of $2$. 
The question, revised to include the condition $q\gt p$, is closely related to Artin's Conjecture. It is a consequence of a result of Heath-Brown that there are at most two primes $p$ for which there is no prime $q\gt p$ such that $p$ is a primitive root of $q$. 
Added: The Heath-Brown paper does not seem to be available online. Murty has a good survey article.
