In this paper we study the value distribution of the least primitive
root to a prime
modulus, as the modulus varies. For each odd prime number p, we
shall denote by
g(p) and G(p) the least primitive
root and the least prime primitive root (mod p),
respectively. Numerical examples show that, in most cases, g(p)
and G(p) are very
small (cf. §4). We can support this observation by a probabilistic
argument
[14, §1].
In fact, on the assumption of a good distribution of the primitive residue
classes
modulo p, we can surmise that
formula here
where π(x) denotes the number of primes not exceeding x.