(The Sieve of Eratosthenes) A prime integer is any integer that is evenly divisible only by itself and 1. The Sieve of Eratosthenes is a method of finding prime numbers. It operates as follows:
a) Create an array with all elements initialized to 1 (true). array elements with prime subscripts will remain 1. All other array elements will eventually be set to zero. You’ll ignore elements 0 and 1 in this exercise.
b) Starting with array subscript 2, 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 subscript is a multiple of the subscript for the element with value 1. For array subscript 2, all elements beyond 2 in the array that are multiples of 2 will be set to zero (subscripts 4, 6, 8, 10, etc.); for array subscript 3, all elements beyond 3 in the array that are multiples of 3 will be set to zero (subscripts 6, 9, 12, 15, etc.); and so on.
When this process is complete, the array elements that are still set to one indicate that the subscript is a prime number. These can then be printed. Write a program that uses an array of 1000 elements to determine and print the prime numbers between 2 and 999. Ignore element 0 of the array.
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