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.Text;
using System.Collections.Generic;
using System.Linq;
using E = System.Linq.Enumerable;

class Program
{
    static void Main(string[] args)
    {
        var X = long.Parse(Console.ReadLine());
        var syugo = SieveOfEratosthenes(100090).Where(n => n  >= X).Min();
        
        Console.WriteLine(syugo);
      
    }
  
    static List<long> SieveOfEratosthenes(long N){
  var Primes = new List<long>();
  if(N > 0){
    var IsPrime = new bool[N+1];
    for(long i = 0;i <= N ;i++){
      IsPrime[i] = true; 
    }
    //0と1は消しておく
    IsPrime[0] = false;
    IsPrime[1] = false;
    for(long i = 2; i <= (long)Math.Sqrt(N);i++){
      if(IsPrime[i]){
        long j = i*2;
        for(long k = j;k <= N;k+=i){
          IsPrime[k] = false;
        }
      }
    }
    for(long i = 1;i <= N ;i++){
      if(IsPrime[i]){
        Primes.Add(i);
      }
    }
  }
  return Primes;
}

}