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;
 
typedef long long int ll;
typedef long double ld;

vector <ll> vec;
ll prime[200000];

void sieve(ll n)
{
	for(ll i=2;i<n;i++)
	{
		if(prime[i]==-1)
		{
			vec.push_back(i);
			for(ll j=2;j*i<n;j++)
			{
				prime[i*j] = 1;
			}
		}
	}
}

int main()
{
    std::ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    
    memset(prime,-1,sizeof(prime));
    sieve(200000);
    
    ll x;
    cin>>x;
    cout<<*lower_bound(vec.begin(),vec.end(),x);
    
}