// Write a function that finds the smallest divisor d>1 of given integer n>1.

using System;

using System.Diagnostics;

​

public class Program

{

    static public int SmallestDivisor(int n)

    {

        Trace.Assert(n > 1);

        return SmallestDivisorInRange(n, 2);

    }

    // Input: 1 < d <= n

    // Returns the smallest divisor of n in range d..n

    // Completion: n - d is not negative and decreases by 1 in each nested call

    static public int SmallestDivisorInRange(int n, int d)

    {

        if(n % d == 0)

            return d;

​

        // d != n => d < n => d+1 <= n

        return SmallestDivisorInRange(n, d + 1); 

    }

    static public void Main()

    {

        for(int n=2; n < 32; n++)

            Console.WriteLine("Smallest divisor of {0} is {1}", n, SmallestDivisor(n));

    }

}