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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;
bool p(int n)
{
    if(n%2==0 || n%3==0)
    {
        return false;

    }
    for(int i=5; i*i<=n; i+6)
    {
        if (n%i ==0||n%(i+2) == 0)
        {
            return false;
        }
    }
}
int np(int n)
{
    bool x=false;
    while(!x)
    {
        n++;
        if(p(n))
        {
            x=true;
        }
    }
    cout<<n;
}
int main()
{
    int n;
    cin>>n;
    if(n==2 || n==3 )
    {
        cout<<n<<endl;
        return 0;
    }
    if(p(n))
    {
        cout<<n<<endl;
        return 0;
    }
    np(n);
    return 0;
}