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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp3
{
    class Program
    {
        static void Main(string[] args)
        {
            var primes = Primes(10000);

            var X = int.Parse(Console.ReadLine());

            var prime = primes.SkipWhile(x => x < X).First();

            Console.WriteLine(prime);
        }
        static IEnumerable<int> Primes(int maxnum)
        {
            int[] sieve = Enumerable.Range(0, maxnum + 1).ToArray();
            sieve[1] = 0; 
            int squareroot = (int)Math.Sqrt(maxnum);
            for (int i = 2; i <= squareroot; i++)
            {
                if (sieve[i] <= 0)
                    continue;
                for (int n = i * 2; n <= maxnum; n += i)
                    sieve[n] = 0;
            }
            return sieve.Where(n => n > 0);
        }
    }
}