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 main() {
	let x: u64 = read();
	if x == 2 {
		println!("2");
	} else {
		println!("{}", ans(x));
	}
}

fn ans(n: u64) -> u64 {
	let mut k = n-1;
	let m = (n as f64).sqrt().ceil() as u64;
	let p = primes(m);
	'outer: loop {
		k += 1;
		for i in &p {
			if k % i == 0 { continue 'outer; }
		}
		break;
	}
	k
}

fn primes(n: u64) -> Vec<u64> {
	let mut v = Vec::new();
	let mut k = 1;
	if n >= 2 { v.push(2); }
	'outer: while k+2 <= n {
		k += 2;
		'inner: for i in &v {
			if (*i)*(*i) > k {
				break 'inner;
			} else if k % *i == 0 {
				continue 'outer;
			}
		}
		v.push(k);
	}
	v
}

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