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<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define mod 1e9+7;

int main()
{
	ll n;
	cin>>n;
	vector<ll> arr(2*n+1,1);
	arr[0]=0;
	arr[1]=0;
	for(ll i=2;i*i<=2*n;i++)
	{
		if(arr[i]==1)
		{
			for(ll j=i*i;j<=2*n;j+=i)
			{
				arr[j]=0;
			}
		}
	}
	ll i=n;
	while(arr[i]==0)
	{
		i++;
	}
	cout<<i<<endl;
	return 0;
}