# 204. Count Primes question

• Here is my solution to the Count Primes question

public class Solution {
public int countPrimes(int n) {
boolean[] isPrime = new boolean[n];
for (int i = 0; i < n; i ++) {
isPrime[i] = true;
}

for (int i = 2; i * i < n; i ++) {
if (isPrime[i]) {
System.out.println(i*i);
for (int j = i; i * j < n; j++) {
isPrime[i * j] = false;
}
}
}
int count = 0;
for (int k = 2; k < n; k ++) {
if (isPrime[k]) count++;
}
return count;

}
}

I am wondering why do i need the "i*i < n" condition in the second loop? If I only use "i < n", the following "isPrime[i]" should be still in the correct bound, but it throws "java.lang.ArrayIndexOutOfBoundsException: -2146737495".

I guess it is because i is too large in this case so i * j becomes a negative number. However, shouldn't "i * i" also become negative in this case? Then why the code above still works?

• Probably it becomes negative after the first iteration, like ii is fine, i(i+k) out of bounds.

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