A prime number is any integer greater than 1 that is evenly divisible only by it

ID: 3547581 • Letter: A

Question

A prime number is any integer greater than 1 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 a primitive type boolean array with all elements initialized

to true. Array elements with prime indices will remain true. All other

array elements will eventually be set to false.

b) Starting with array index 2, determine whether a given element is

true. If so, loop through the remainder of the array and set to false

every element whose index is a multiple of the index for the element

with value true. Then continue the process with the next element with

value true. For array index 2, all elements beyond element 2 in the

array that have indices which are multiples of 2 (indices 4, 6, 8, 10,

etc.) will be set to false; for array index 3, all elements beyond

element 3 in the array that have indices which are multiples of 3

(indices 6, 9, 12, 15, etc.) will be set to false; and so on. When

this process completes, the array elements that are still true

indicate that the index is a prime number. These indices can be

displayed. Write an application that uses an array of 1000 elements

to determine and display the prime numbers between 2 and 999. Ignore

array elements 0 and 1.

a) public static void main(String[] args) {

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