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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>

using namespace std;

int main()
{
	int X;
	
	cin >> X;
	
	if(X < 4)
		cout << X << '\n';
		
	else
	{
		vector<int> primos {3};
		
		for(int k = 5; k <= 100003; k += 2)
		{
			bool is_prime = true;
			
			for(int i = 0; 1LL * primos[i] * primos[i] <= k; ++i)
			{
				if(k % primos[i] == 0)
				{
					is_prime = false;
					break;
				}
			}
			
			if(is_prime)
			{
				if(k >= X)
				{	
					cout << k << '\n';
					break;
				}
				
				primos.push_back(k);
			}
		}
	}
		
 	return 0; 
}