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: Accepted)

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

namespace ConsoleApp
{
    class Program
    {
        static void Main(string[] args)
        {
            var X = int.Parse(Console.ReadLine());
            var primeList = new List<int>() { 2 };

            var ans = X;
            while (true)
            {
                SetPrime((int)Math.Sqrt(ans) + 1, primeList);
                if (primeList.Contains(ans) || primeList.All(s => ans % s != 0))
                {
                    Console.WriteLine(ans);
                    return;
                }
                ans++;
            }
        }

        static void SetPrime(int n, List<int> primeList)
        {
            var last = primeList.Last();
            if (last >= n) return;

            for (int i = last + 1; i <= n; i++)
            {
                if (primeList.All(s => i % s != 0)) primeList.Add(i);
            }
        }
    }
}