Problem:
Score: 300 points

Problem Statement

Find the minimum prime number greater than or equal to X.

Notes

A prime number is an integer greater than 1 that cannot be evenly divided by any positive integer except 1 and itself.

For example, 2, 3, and 5 are prime numbers, while 4 and 6 are not.

Constraints

2 \le X \le 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X

Output

Print the minimum prime number greater than or equal to X.

Sample Input 1

20

Sample Output 1

23

The minimum prime number greater than or equal to 20 is 23.

Sample Input 2

2

Sample Output 2

2

X itself can be a prime number.

Sample Input 3

99992

Sample Output 3

100003

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

namespace AtCoderCs
{
    class Program
    {
        static void Main()
        {

            var Num = int.Parse(Console.ReadLine());
            var End = (int)Math.Sqrt(Num) + 2;
            var Continue = true;

            if (Num == 2) Console.WriteLine(2);
            else if (Num % 2 == 0) Num++;

            for (; Continue; Num += 2)
            {

                for (int i = 3; i < End; i += 2)
                {

                    if (Num % i == 0)
                    {
                        Continue = false;
                        break;
                    }

                }

                Continue = !Continue;

                if (Continue)
                {

                    Num += 2;
                    if (End * End < Num)
                        End++;

                }

            }

            Console.WriteLine(Num);

        }

    }
}