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 <algorithm>
#include <bitset>
#include <boost/multiprecision/cpp_int.hpp>
#include <algorithm>
#include <climits>
#include <cmath>
#include <cstring>
#include <functional>
#include <iostream>
#include <list>
#include <map>
#include <set>
#include <numeric>
#include <sstream>
#include <stdio.h>
#include <string>
#include <tuple>
#include <vector>
#include<iomanip>
namespace mp = boost::multiprecision;
using namespace std;
using ull = unsigned long long;
using ld = long double;
using lll = boost::multiprecision::cpp_int;
using ll = long long;
#define FOR(i, N) for(ll i = 0; i < N; ++i)

#define ALL(v) (v).begin(), (v).end()
#define RALL(v) (v).rbegin(), (v).rend()
// using int = ll;
ll gcd(ll m, ll n) {
    if(n == 0)
        return abs(m);
    return (gcd(n, m % n));
}
void putYN(bool b) {
    if(b) {
        cout << "Yes" << endl;
    } else {
        cout << "No" << endl;
    }
}
ll combi(ll n, ll k) {
    ll r = 1, rr = 1;
    for(ll i = 0; i < k; ++i) {
        r *= (n - i);
        rr *= (i + 1);
        // r %= 1000000007;
        // rr %= 1000000007;
    }
    r /= rr;
    // r %= 1000000007;
    return r;
}
int main(){
  ll X;
  cin>>X;
  vector<bool> A(200001,true);
  for(int i=2;i<=200000;++i){
    if(A[i]==false)continue;
    for(int j=i*2;j<=200000;j+=i){
      A[j]=false;
    }
  }
  for(int i=X;i<200000;++i){
    if(A[i]==true){
      cout<<i<<endl;
      break;
    }
  }
  return 0;
}