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 <bits/stdc++.h>
using namespace std;

int main() {
    int n;
    cin>>n;
    
    bool prime[100005]; 
    
    vector<int> vp;
    memset(prime, true, sizeof(prime)); 
  
    for (int p=2; p*p<=100001; p++){
        if (prime[p] == true){
            for (int i=p*p; i<=100001; i+=p){
                prime[i] = false; 
            }
        } 
    }
    
    for(int i=2; i<=100001; i++){
        if(prime[i] == true){
            vp.push_back(i);
        }
    }
    
    // for(int i=0; i<10; i++) cout<<vp[i]<<" ";
    
    cout<<*lower_bound(vp.begin(),vp.end(),n);
    
    
	return 0;
}