Problem #3 on Project Euler is:
The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143?
My solution takes forever. I think I got the right implementation; however, when testing with the big number, I have not being able to see the results. It runs forever. I wonder if there's something wrong with my algorithm:
public class LargestPrimeFactor3 {
    public static void main(String[] args) {
        long start, end, totalTime;
        long num = 600851475143L;
        long pFactor = 0;
        start = System.currentTimeMillis();
        for(int i = 2; i < num; i++) {
            if(isPrime(i)) {                
                if(num % i == 0) {
                    pFactor = i;                        
                }
            }
        }
        end = System.currentTimeMillis();
        totalTime = end - start;
        System.out.println(pFactor + " Time: "+totalTime);
    }
    static boolean isPrime(long n) {
        for(int i = 2; i < n; i++) {
            if(n % i == 0) {
                return false;
            }
        }        
        return true;
    }     
}
                Although not in Java, I think you can probably make out the following. Basically, cutting down on the iterations by only testing odd divisors and up to the square root of a number is needed. Here is a brute force approach that gives an instant result in C#.
static bool OddIsPrime (long oddvalue)  // test an odd >= 3 
{
    // Only test odd divisors.
    for (long i = 3; i <= Math.Sqrt(oddvalue); i += 2)
    {
        if (value % i == 0)
            return false;
    }
    return true;
}
static void Main(string[] args)
{
    long max = 600851475143;   // an odd value
    long maxFactor = 0;
    // Only test odd divisors of MAX. Limit search to Square Root of MAX.
    for (long i = 3; i <= Math.Sqrt(max); i += 2)
    {
        if (max % i == 0)
        {
            if (OddIsPrime(i))  // i is odd
            {
                maxFactor = i;
            }
        }
    }
    Console.WriteLine(maxFactor.ToString());
    Console.ReadLine();
}
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