Possible optimization in my code?

Question

In order to solve the Euler Project problem n°5, I wrote the following program:

class p5
{
    const int maxNumber = 20;
    static void Main(string[] args)
         


        

Answer 1

Using Enumerable is slow (see this for comparison of Enumerable.Repeat and for loop for initialization of an array). Try plain while/for loop like this:

        int maxNumber = 21;
        int n = 1;
        bool found = false;
        while(!found)
        {
            found = true;
            for(int i = 1; i < maxNumber; i++)
            {
                if(n % i != 0)
                {
                    found = false;
                    break;
                }
            }
            n++;
        }
        return n-1;

This runs for about 4 seconds on my computer in debug.

EDIT

When considering further optimizations, it is better to start testing modulo of larger numbers, so when I changed the for loop to:

for (int i = maxNumber; i > 1; i--)

the time dropped to under 2 seconds.

A mathematical insight would be that we only have to test divisibility by numbers that are not multiples of the numbers we already tested. In our case we can write:

    private int[] p = { 19, 17, 16, 13, 11, 9, 7, 5, 4, 3, 2 };
    int Job()
    {
        int n = 1;
        bool found = false;
        while (!found)
        {
            found = true;
            foreach (int i in p)
            {
                if (n % i != 0)
                {
                    found = false;
                    break;
                }
            }
            n++;
        }
        return n - 1;
    }

However, this is actually slower, about 2.5 seconds.