Prime numbers are important as the building blocks for the set of all natural numbers, because prime factorisation is an important and useful property of all natural numbers. Students can discover them by using the method known as the Sieve of Eratosthenes, named after the Greek geographer and astronomer who lived from c. 276-194 BC. Eratosthenes was also famous for being the first to scientifically calculate the Earth's circumference, which he did correctly to within 80 km. In this article, the author illustrates Eratosthenes' method for obtaining the primes. (Contains 1 figure.)