Sieve of Eratosthenes Issue Java

Question

I've got an issue with an assignment that I have requiring the use of arrays. I need to create the Sieve of Eratosthenes algorithm and print out all the prime numbers. I'm quite confused because as far as I can tell, my order of operations is correct. Here is the code:

        //Declare the array
        boolean numbers [] = new boolean[1000];
        int y = 0;

        //Declare all numbers as true to begin
        for(int i = 2; i < 1000;i++){
            numbers[i] = true;
        }
        //Run loop that increases i and multiplies it by increasing multiples
        for (int x = 2; x < 1000; x++) {

            //A loop for the increasing multiples; keep those numbers below 1000
            //Set any multiple of "x" to false
            for(int n = 2; y < 1000; n++){
            y = n * x;
            numbers[y] = false;
            }
        }

I first set all the numbers in the array to true. Then the second loop will start "x" at 2, then inside it is a nested loop that will multiply "x" by values of "n" and "n" will continue to increase as long as the product of that multiplication ("y") is below 1000. Once "y" reaches that maximum, "x" will go up one number and the process repeats until all non-prime numbers are set to false.

That was my logic when I made the code, but when I try to run it I get the "ArrayIndexOutOfBoundsException" error. From what I can tell I set everything to stay below 1000 so it shouldn't be going over the array size.

I know its probably not the most efficient algorithm because as "x" increases it will go over numbers it already went over but it was the most simple one I could think of.

Answer 1

Here:

        for(int n = 2; y < 1000; n++){
        y = n * x;
        numbers[y] = false;
        }

you first check that y < 1000, and then intialize and use it. This is the wrong way around.

Also, you can get away with running the above loop only when x is prime. This won't affect correctness, but should make your code much faster.