The sieve of Eratosthenes is a useful method for making a list of prime numbers. Let d and n be positive integers. We say that d divides n, or that d is a divisor of n, if the fraction n/d is an integer. For example, 4 divides 12 and 1 divides 17, but 3 does not divide 14. The set of divisors of 12 is {1, 2, 3, 4, 6, 12}, and the set of divisors of 17 is {1, 17}. Sometimes it is important to include negative integers in a discussion of divisors. But in this article we will consider only positive integers and positive divisors. A positive integer n > 1 is called a prime number if the only divisors of n are 1 and n. A positive integer n >1 is said to be a composite number if it is not prime. The sequence of prime numbers begins with 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41,.... Prime numbers are important in number theory because every positive integer...