Theory of numbers: Prime tests

This lecture is part of an online undergraduate course on the theory of numbers. We describe how to use Fermat's theorem as a test to see if numbers n are not prime, by checking to see if a^n=a mod n for various numbers a. We then given an example of a "Carmichael number": a composite number that passes this probabilistic test for primeness. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52Qf7lc3HHvHRdIysxEcj1H