java - for loop finding the prime numbers

Question

I am trying to run this code to print the sum of all the prime numbers less than 2 million. This loop is never ending. Can anyone tell me what is wrong with the code? It seems to work with smaller numbers though.

public static void main(String[] args) {

        long result = 1;

        for(int i=0; i<2000000; i++) {
            if(isPrime(i)) {
                result+= i;
            }
        }
        System.out.println(result);

    }
private static boolean isPrime(long n) {
    boolean result = false;

    for(long i=2; i<(long)Math.sqrt(n); i++) {
        if(n%i == 0) {
            result = false;
            break;
        }
        else result = true;
    }
    return result;
}

Answer 1

In isPrime you are only testing division by 2:

private static boolean isPrime(long n) {
    boolean result = false;

    for(long i=1; i<n/2; i++) {
        if(n%2 == 0) {
            result = false;
            break;
        }
        else result = true;
    }
    return result;

}

it should be division by every i and starting from 2:

for(long i=2; i<n/2; i++) {
    if(n%i == 0) {
      ...

Practically in your current version an odd number n will keep dividing by 2 up to n/2 instead of stopping much sooner. Consider n = 21. You are dividing by 2 from 1 to 10, instead of dividing by 3 at the 3rd step and exiting.

It not only gives incorrect results, but also takes much longer than needed to reach a return statement.

Edit: For faster results check out this sieve of Erathostenes method:

public static long sumOfPrimes(int n) {

    long sum = 0;

    boolean[] sieve = new boolean[n];
    for(int i = 2; i < Math.sqrt(n); i++) {
        if(!sieve[i]) {
            for(int j = i * i; j < n; j += i) {
                sieve[j] = true;
            }
        }
    }

    for(int i = 2; i < n; i++) {
        if(!sieve[i]) {             
            sum += i;
        }
    }

    return sum;
}

Edit #2: Found some bugs with your new version. Here's the corrected one:

private static boolean isPrime(long n) {
    boolean result = false;

    if(n == 2 || n == 3) return true;

    for (long i = 2; i <= (long) Math.sqrt(n); i++) {
        if (n % i == 0) {
            result = false;
            break;
        } else
            result = true;
    }

    System.out.println(n + " " + result);
    return result;
}