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 (1.15.1) (judge verdict: Accepted)

use std::io;
use std::str::FromStr;

fn input<T:FromStr>() -> T {
    let mut line: String = String::new();
    io::stdin().read_line(&mut line);
    line.trim().parse().ok().unwrap()
}



fn main() {
    let x: u64 = input();
    let mut prime_numbers: Vec<u64> = Vec::new();
    for i in 2..((x+1) as f64).sqrt().ceil() as u64 {
        let mut flag = true;
        for n in &prime_numbers {
            if i % n == 0 {
                flag = false;
            }
        }
        if flag {
            prime_numbers.push(i);
        }
    }
    // println!("{:?}", prime_numbers);
    let mut res = x;
    loop {
        let mut flag = true;
        for n in &prime_numbers {            
            if res % n == 0 {
                flag = false;
            }
        }
        if flag {
            println!("{}", res);
            return;
        }
        res += 1;
    }
}