Chapter 6, Problem 6.30E

(The Sieve of Eratosthenes) A prime integer is any integer greater than 1 that can be divided evenly only by itself and 1. The Sieve of Eratosthenes is a method of finding prime numbers. It works as follows:

1. Create an array with all elements initialized to 1 (true). Array elements with prime indices will remain 1. All other array elements will eventually be set to zero.
2. Starting with array index 2 (index 1 is not prime), every time an array element is found whose value is 1, loop through the remainder of the array and set to zero every element whose index is a multiple of the index for the element with value 1. For array index 2, all elements beyond 2 in the array that are multiples of 2 will be set to zero (indices 4, 6, 8, 10, and so on.). For array index 3, all elements beyond 3 in the array that are multiples of 3 will be set to zero (indices 6, 9, 12, 15, and so on.).

When this process is complete, the array elements that are still set to 1 indicate that the index is a prime number. Write a program that uses an array of 1,000 elements to determine and print the prime numbers between 1 and 999. Ignore element 0 of the array.