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;
using System.Text;
using System.Threading.Tasks;
using System.Windows;

namespace AtCoder
{
    static class Program
    {
        static void Main()
        {
            //ここから
            var X = IO.ReadLineToInt();
            List<int> num = new List<int>();
            int ans = 0;

            for (int i = 0; i < X - 2; i++)
            {
                num.Add(X % (i + 2));
            }
            if (num.All(n => n != 0))
            {
                ans = X;
            }
            else
            {
                for (int i = 0; i < X - 2; i++)
                {
                    num[i] = i + 2 - num[i];
                }
                num.Add(0);
                num = num.OrderBy(n => n).Distinct().ToList();
                for (int i = 0; i < num.Count -1; i++)
                {
                    if (num[i + 1] - num[i] > 1)
                    {
                        ans = X + num[i] + 1;
                        break;
                    }
                }
            }

            //ここまで

            Console.WriteLine(ans);
            Console.ReadKey();
        }

    }

    static class Func
    {
        static public long mod = 1000000007;
        static public void Swap<T>(ref T a, ref T b) { T temp = a; a = b; b = temp; }
        static public long GCD(long a, long b) { return b != 0 ? GCD(b, a % b) : a; }
        static public long LCM(long a, long b) { return (long)a * b / GCD(a, b); }
        static public long Factorial(long a) { return a == 1 ? a : a * Factorial(a - 1); }


        public static double ToAngle(this double radian)
        {
            return (double)(radian * 180 / Math.PI);
        }

        public static double ToRadian(this double angle)
        {
            return (double)(angle * Math.PI / 180);
        }

        static public long Conbination(long n, long m)
        {
            if (m == 0) return 1;
            if (n == 0) return 0;
            return n * Conbination(n - 1, m - 1) / m;
        }

        static public void Factoring(long num, ref long[] vs)
        {
            if (num == 1)
            {
                vs[1]++;
            }
            for (long i = 2; i < Math.Sqrt(num); i++)
            {
                if (num % i == 0)
                {
                    vs[i]++;
                    Factoring(num / i, ref vs);
                }
            }
            vs[1]++;
        }
    }

    static class IO
    {
        static public string ReadLineToString() { return Console.ReadLine(); }

        static public int ReadLineToInt() { return int.Parse(Console.ReadLine()); }
        static public long ReadLineToLong() { return long.Parse(Console.ReadLine()); }
        static public List<string> ReadLineToStringList() { return Console.ReadLine().Split(' ').ToList(); }

        static public List<int> ReadLineToIntList() { return Console.ReadLine().Split(' ').Select(int.Parse).ToList(); }
        static public List<long> ReadLineToLongList() { return Console.ReadLine().Split(' ').Select(long.Parse).ToList(); }

        static public List<double> ReadLineToDoubleList() { return Console.ReadLine().Split(' ').Select(double.Parse).ToList(); }

        static public void WriteStrings(object[] strings) { foreach (var o in strings) { Console.Write(o + " "); } }
    }
}