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)

fn input_one<T: std::str::FromStr> () -> Result<T, T::Err> {
    let mut n = String::new();
    std::io::stdin().read_line(&mut n).unwrap();
    n.trim().parse()
}

fn get_primes(n: usize) -> Vec<usize> {
    let mut spf = vec![None; n+1];
    let mut is_prime = vec![true; n+1];
    let mut primes = Vec::new();

    is_prime[0] = false;
    is_prime[1] = false;

    for i in 2..n+1 {
        if is_prime[i] {
            primes.push(i);
            spf[i] = Some(i);
        }
        for &prime in primes.iter() {
            if i * prime >= n + 1 || prime > spf[i].unwrap() {
                break;
            }

            is_prime[i * prime] = false;

            spf[i * prime] = Some(prime);
        }
    }
    primes
}

fn main() {
    let x: usize = input_one().unwrap();
    println!("{}", get_primes(100003).into_iter().skip_while(|&a| a < x).next().unwrap());
}