Least primitive root of prime numbers

Let p be a prime number. Fermat's little theorem [1] states that a^(p-1) mod p=1 (a hat (^) denotes exponentiation) for all integers a between 1 and p-1. A primitive root [1] of p is a number r such that any integer a between 1 and p-1 can be expressed by a=r^k mod p, with k a nonnegative integer smaller that p-1. If p is an odd prime number then r is a primitive root of p if and only if r^((p-1)/q) mod p>1 for all prime divisors q of p-1. If a number r can be found that satisfies these conditions, then p must be a prime number. In fact, it is possible to relax the above conditions in order to prove that p is prime [2]; it is sufficient to find numbers r_k (r_k denotes the variable r with index k) such that (r_k)^((p-1)/q_k) mod p>1 and (r_k)^(p-1) mod p=1 for all prime divisors q_k of p-1 (these conditions guarantee the existence of a primitive root of p).