I know we've learned a lot about primitive roots and how to find them along with the order of integers but why do we want to know this? Do we know anything special about a number that has primitive roots compared to those that don't? Is there any sort of important connection between the composite numbers that have primitive roots compared to every prime since they all have primitive roots?

These were just a few questions that popped into my head when reviewing what we've learned. I've had trouble looking up interesting facts about primitive roots and I searched to see the importance of primitive roots and was unsuccessful. Please let me know!