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 JavaScript (node.js v5.12) (judge verdict: Accepted)

"use strict";
const fs = require("fs");

const X = parseInt(fs.readFileSync("/dev/stdin", { encoding: "utf8" }));

function isPrime(n) {
  const m = Math.ceil(Math.sqrt(n));
  for (let i = 2; i < m; ++i) {
    if (n % i === 0) {
      return false;
    }
  }
  return true;
}

function main() {
  let i = X;
  while (true) {
    if (isPrime(i)) {
      return i;
    }
    i++;
  }
}

console.log(main());