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

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("Failed to read bytes") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn main() {
    let x:usize = read();
    let v= primes(x);
    for i in v {
        if i >= x {
            println!("{}", i);
            break;
        }
    }
}

fn primes(n:usize) -> impl Iterator<Item = usize> {
    const START: usize = 2;
    if n < START {
        Vec::new()
    } else {
        let mut is_prime = vec![true; 100005];
        let limit = 100005;
        for i in START..=limit + 1 {
            let mut it = is_prime[i - START..].iter_mut().step_by(i);
            if let Some(true) = it.next() {
                it.for_each(|x| *x = false);
            }
        }
        is_prime
    }
    .into_iter()
    .enumerate()
    .filter_map(|(e, b)| if b { Some(e + START)} else { None })
}