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::Write;

#[allow(unused)]
macro_rules! debug {
    ($($format:tt)*) => (write!(std::io::stderr(), $($format)*).unwrap());
}
#[allow(unused)]
macro_rules! debugln {
    ($($format:tt)*) => (writeln!(std::io::stderr(), $($format)*).unwrap());
}

fn main() {
    let x: usize = {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).unwrap();
        let s = s.trim_right().to_owned();
        s.parse().unwrap()
    };

    let primes = prime_sieve(2 * x);
    let mut ans = 0;
    for p in primes {
        if p >= x {
            ans = p;
            break;
        }
    }
    println!("{}", ans);
}

fn prime_sieve(n: usize) -> Vec<usize> {
    let mut table: Vec<usize> = vec![0; (n + 1) as usize];
    let mut primes: Vec<usize> = Vec::new();

    for i in 2..(n+1) {
        if table[i as usize] == 0 {
            primes.push(i);
            for j in 2..n {
                if i * j > n {
                    break
                }
                table[(i * j) as usize] = 1
            }
        }
    }

    primes
}