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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::{fastout, input};
use std::cmp::min;
const MAX: usize = 100004;

#[fastout]
fn main() {
    input! {
        x: usize,
    }
    let mut table = vec![true; MAX];
    for i in 2..min(x, 317) {
        if !table[i] {
            continue;
        }
        for j in (i..MAX).step_by(i).filter(|j| *j >= x) {
            table[j] = false;
        }
    }
    println!("{}", (x..MAX).find(|i| table[*i]).unwrap());
}