Find the sum of all the primes below two million.My program doesn't work for very big numbers

Question

This is my code for finding the sum of primes.It works good with some low numbers but if it's 2000000(2 million) it never ends.Anybody can help me?

import java.math.BigInteger;
public class Problem010{
    public static void main(String[] args) {

        BigInteger sum = new BigInteger("2");

        //for (int i=3; i<2000000; i++) {
        for(int i=3; i<10; i++){
            for (int j=2; j<i; j++){
                if (i % j == 0) 
                    break;
                else if (i == j+1){
                    sum = sum.add(BigInteger.valueOf(i));
                }
            }
        }
        System.out.println("Sum  = "+sum); 
    }
}

Answer 1

your answer is 142913828922 but how?

I just changed your algorithm a little bit:

public static void main(String[] args) {

    BigInteger sum = new BigInteger("2");
    boolean isPrime = true;
    for (int i=3; i<2000000; i++) {
    double aa = Math.sqrt((double)i);
        for (int j=2; j<=aa; j++){
            if (i % j == 0){ 
                isPrime = false;
                break;
            }
        }
        if(isPrime){
            sum = sum.add(BigInteger.valueOf(i));
        }
        isPrime = true;
    }
    System.out.println("Sum  = "+sum); 
}

instead of going through all the numbers from 2 to i I just go from 2 to sqrt(i) and this improve your code running time a lot :)

Answer 2

@Lrrr, answer is correct. But algorithm can be further optimised. Look at my isPrime algorithm. For 2 million you don't need the BigInteger.

    long sum = 2;// new BigInteger("2");
    for (int i=3; i<2000000; i++) {
        if(isPrime(i)) {
            sum = sum + i;//.add(BigInteger.valueOf(i));
        }    
    }
    System.out.println("Sum  = "+sum);

Here is isPrime method.

 static boolean isPrime(int n) {
    if (n < 2) {
        return false;
    }
    if (n == 2 || n == 3) {
        return true;
    }
    if ((n & 1) == 0 || n % 3 == 0) {
        return false;
    }
    int sqrtN = (int) Math.sqrt(n) + 1;
    for (int i = 6; i <= sqrtN; i += 6) {// loop 6 step
        if (n % (i - 1) == 0 || n % (i + 1) == 0) {
            return false;
        }
    }
    return true;
}