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;
  int p[int(2e5+1)]={};
  for(int i=2;i<=2e5;i++){
    int k=1;
    while(i*k<=2e5){
      p[i*k]++;
      k++;
    }
  }
  for(int i=2;i<=2e5;i++){
    if(p[i]==1&&x<=i){
      cout << i << endl;
      return 0;
    }
  }
}