Do all prime numbers have primitive roots?

Could you clarify, are you asking if every prime number possesses at least one primitive root? It's a fascinating question that delves into the realm of number theory. Prime numbers, by definition, have only two distinct divisors: one and themselves. But do these numbers inherently possess a special number, known as a primitive root, which generates all the non-zero residues modulo that prime when raised to various powers? Let's explore the intricacies of this query together.