(The Sieve of Eratosthenes) A prime integer is an integer that is evenly divisible by only itself and 1. The Sieve of Era- tosthenes is an algorithm for finding prime numbers. It operates as follows:

Question

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.
b) Starting with array subscript 2 (subscript 1 must be 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 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
subscripts can then be printed. Write a script that uses an array of 1000 elements to determine and print the prime numbers
between 1 and 999. Ignore element 0 of the array.

Answer 1

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