According to wikipedia, "In modular arithmetic, a branch of number theory, a **primitive root modulo n** is any number g with the property that any number coprime to n is congruent to a power of g (mod n). That is, if g is a primitive root (mod n), then for every integer a that has gcd(a, n) = 1, there is an integer k such that gk ≡ a (mod n). k is called the index of a."

Again, primitive roots is used in cryptology. Most specifically in regards to the Diffie-Hellman Key Exchange Scheme. This Scheme is "a cryptographic protocol that allows two parties that have no prior knowledge of each other to jointly establish a shared secret key over an insecure communications channel." It is thought this that users may freely share their public keys over insecure transmission channels without fear of compromising the cryptosystem.