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 ;

int main(){
  int x ; cin >> x ;
  if(x==2){
    cout << 2 << endl ;
    return 0 ;
  }
  if(x==3){
    cout << 3 << endl ;
    return 0 ;
  }
  vector<int> prime ;
  prime.push_back(2) ;
  prime.push_back(3) ;
  for(int i=5;i<1000000;i+=2){
    bool check = true ;
    for(int j=0;j<prime.size();j++){
      if(i%prime.at(j)==0){
        check = false ;
        break ;
      }
    }
    if(check){
      if(i>=x){
        cout << i << endl ;
        return 0 ;
      }else{
        prime.push_back(i) ;
      }
    }
  }
}