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: Wrong Answer)

#include<iostream>
#include<vector>
#include<algorithm>
#include<string>
#include<numeric>
#include<utility>

using namespace std;

typedef long long int ll;
const int INF = 1<<30;
const long long LINF = 1LL<<60;

int main(){
    int x;
    cin >> x;
    int ans = 0;
    if(x == 2){
        cout << 2 << endl;
        return 0;
    }else if(x % 2 == 0){
        x += 1;
    }else{
        x += 2;
    }
    while(1){
        bool f = true;
        for(int i = 3; i * i <= x; i += 2){
            if(x % i == 0){
                f = false;
                break;
            }
        }
        if(f){
            break;
        }
        x += 2;
    }
    cout << x << endl;
    return 0;
}