ABSTRACT
This chapter provides an understanding of prime numbers in various integer rings. An integer that is not a unit is a prime if it can’t be written as a product unless one factor is a unit. Although it would be reasonable to say that units are primes, instead of explicitly excluding them, that is not usually done. The chapter provides the Euclid’s celebrated proof of the infinitude of primes by using a theorem that shows not only that there are infinitely many primes, but that there are infinitely many primes of a certain kind. The most important feature of a prime is whether it is even or odd. The chapter presents a discussion on Gaussian primes and proves a useful lemma about when a Gaussian integer divides an integer.
