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

public class Prime
{
    BitArray Sieve;
    // Sieve of Eratosthenes
    public void Init(int max)
    {
        Sieve = new BitArray(max + 1);
        var end = (int)(Math.Sqrt(max) + 0.1);
        Sieve.Set(1, true);
        for (int i = 2; i <= end; i++)
        {
            if (!Sieve.Get(i))
            {
                for (int j = i * 2; j <= max; j += i)
                {
                    Sieve.Set(j, true);
                }
            }
        }
    }

    public bool IsPrime(int n)
    {
        return !Sieve.Get(n);
    }

    public int[] GetPrimes(int n)
    {
        return Enumerable.Range(2, n - 1).Where(i => !Sieve.Get(i)).ToArray();
    }
}

public class Solution
{
    public static void Main()
    {
        var x = int.Parse(Console.ReadLine());
        var prime = new Prime();
        prime.Init(1000000);
        while(true)
        {
            if(prime.IsPrime(x))
            {
                Console.WriteLine(x);
                return;
            }
            x++;
        }
    }
}