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 proconio::input;

fn smallest_factor(n: usize) -> usize {
  if n % 2 == 0 { return 2; }
  if n % 3 == 0 { return 3; }
  if n % 5 == 0 { return 5; }

  let mut k = 7;
  for dk in [4,2,4,2,4,6,2,6].iter().cycle() {
    if n % k == 0 { 
      return k; 
    }
    k += dk;
    if k * k >= n {
      return n;
    }
  }
  return n;
}
fn is_prime(n: usize) -> bool {
  smallest_factor(n) == n
}

fn main() {
  input! { 
    x: usize,
  }
  for p in x..2*x {
    if is_prime(p) {
      println!("{}", p);
      break;
    }
  }
}