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

namespace AtCoder
{
	class Program
	{
		public static void Main()
		{
#if TextInput
			using(var reader = new StreamReader(Debug.SampleTextPath)) 
			{
				Console.SetIn(reader);
#endif
				var X = IO.ReadInt();
				while(!Util.IsPrime(X)) { ++ X; }
				IO.Write(X);
#if TextInput
			}
#endif
		}
	}

	public static class IO
	{
		public static string   Read()								 { return Console.ReadLine(); }
		public static string[] ReadArray(char iSplitter = ' ')		 { return Read().Split(iSplitter); }
		public static int	   ReadInt()							 { return int.Parse(Read()); }
		public static int[]	   ReadIntArray(char iSplitter = ' ')	 { return ReadArray().Select(iText => int.Parse(iText)).ToArray(); }
		public static long	   ReadLong()							 { return long.Parse(Read()); }
		public static long[]   ReadLongArray(char iSplitter = ' ')	 { return ReadArray().Select(iText => long.Parse(iText)).ToArray(); }
		public static double   ReadDouble()							 { return double.Parse(Read()); }
		public static double[] ReadDoubleArray(char iSplitter = ' ') { return ReadArray().Select(iText => double.Parse(iText)).ToArray(); }
		public static char	   ReadChar()							 { return Read()[0]; }
		public static char[]   ReadCharArray()						 { return Read().ToCharArray(); }

		public static void Write(string iValue)	 { Console.WriteLine(iValue); }
		public static void Write(int iValue)	 { Console.WriteLine(iValue); }
		public static void Write(long iValue)	 { Console.WriteLine(iValue); }
		public static void Write(double iValue)  { Console.WriteLine(iValue); }
		public static void Write(char iValue)	 { Console.WriteLine(iValue); }
		public static void Write(decimal iValue) { Console.WriteLine(iValue); }
		public static void Write(bool iValue)	 { Console.WriteLine(iValue ? "Yes" : "No"); }
		public static void Write<Type>(IEnumerable<Type> iValue , string iJoinWord = " ") { Console.WriteLine(string.Join(iJoinWord , iValue)); }
	}

	public static class Util
	{
		public static long Gcd(long i0 , long i1) { return (i0 > i1) ? _Gcd(i0 , i1) : _Gcd(i1 , i0); }
		public static long Lcm(long i0 , long i1) { return (i0 * i1) / Gcd(i0 , i1); }
		public static long ModPow(long iBaseNumber , long iPow , long iModNumber)
		{
			var num = 1L;
			while(iPow != 0)
			{
				if((iPow & 0x1) != 0)
				{
					num = (num * iBaseNumber) % iModNumber;
				}
				iBaseNumber = (iBaseNumber * iBaseNumber) % iModNumber;
				iPow >>= 1;
			}
			return num;
		}
		public static long CombinationNum(int iLeftNumber , int iRightNumber)
		{
			if(iRightNumber == 0) { return 1; }
			if(iLeftNumber == 0)  { return 0; }
			return iLeftNumber * CombinationNum(iLeftNumber - 1 , iRightNumber - 1) / iRightNumber;
		}
		public static long Factorial(long iNumber)
		{
			if(iNumber == 0) { return 1L; }
			return iNumber * Factorial(iNumber - 1);
		}
		public static bool IsPrime(long iNumber)
		{
			if(iNumber < 2)			  { return false; }
			else if(iNumber == 2)	  { return true;  }
			else if(iNumber % 2 == 0) { return false; }

			var sqrtNum = Math.Sqrt(iNumber);
			for(var i = 3 ; i <= sqrtNum ; i += 2)
			{
				if(iNumber % i == 0) { return false; }
			}
			return true;
		}
		private static long _Gcd(long i0 , long i1)	{ return (i1 == 0) ? i0 : _Gcd(i1 , i0 % i1); }
	}

	public class UnionFind
	{
		public int[] Parents;
		public int[] RootNums;
		public UnionFind(int iRootNum)
		{
			Parents = Enumerable.Range(0 , iRootNum).ToArray();
			RootNums = new int[iRootNum];
		}
		public void Normalize()
		{
			for(var iIndex = 0 ; iIndex < Parents.Length ; ++ iIndex)
			{
				var rootIndex = _GetRoot(iIndex);
				++ RootNums[rootIndex];
				Parents[iIndex] = rootIndex;
			}
		}
		public void Union(int iNumber0 , int iNumber1)
		{
			var rootNumber0 = _GetRoot(iNumber0);
			var rootNumber1 = _GetRoot(iNumber1);
			if(rootNumber0 < rootNumber1)
			{
				Parents[rootNumber1] = rootNumber0;
			}
			else
			{
				Parents[rootNumber0] = rootNumber1;
			}
		}
		public int _GetRoot(int iNumber)
		{
			return (Parents[iNumber] == iNumber) ? iNumber : _GetRoot(Parents[iNumber]);
		}
	}

	public class CumulativeSum
	{
		public static CumulativeSum Create(IEnumerable<long> iNumbers)
		{
			var numbers = iNumbers.ToArray();
			var cumulativeSum = new CumulativeSum
			{
				Numbers = numbers,
				SumNumbers = new long[numbers.Length + 1]
			};
			var sumNumber = 0L;
			for(var iIndex = 0 ; iIndex < numbers.Length ; ++ iIndex)
			{
				sumNumber += numbers[iIndex];
				cumulativeSum.SumNumbers[iIndex + 1] = sumNumber;
			}
			return cumulativeSum;
		}

		public long[] Numbers { get; private set; }
		public long[] SumNumbers { get; private set; }

		public int GetMaxTotalIndex(int iAreaNum)
		{
			var maxIndex = -1;
			var maxNumber = 0L;
			var num = Numbers.Length - iAreaNum + 1;
			for(var iIndex = 0 ; iIndex < num ; ++ iIndex)
			{
				var checkNumber = SumNumbers[iAreaNum + iIndex] - SumNumbers[iIndex];
				if(maxNumber < checkNumber) 
				{
					maxIndex = iIndex;
					maxNumber = checkNumber;
				}
			}
			return maxIndex;
		}
	}
}