Prime numbers form what is arguably the most important set of numbers. They provide us with fascinating and practical ways to solve a wide variety of number theory problems, many of which we examine in school maths. As we shall see, prime numbers allow us to express integers in unique ways and organize their useful properties. We could barely begin to scratch the surface of number theory without an understanding of prime numbers. While discussing primes, we also identify composite numbers, which make up most of the rest of the natural numbers.