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: Wrong Answer)

function main(input) {
  console.log(nextPrimes(input, [2, 3]).pop())
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));

function nextPrimes(n, ps) {
  if (n == 1 || n == 2) {
    return [2]
  }

  var currentMax = ps[ps.length - 1]
  if (currentMax >= n) return ps;

  var search = true;
  var base = currentMax;
  while (search) {
    var elder = (Math.floor((base + 1) / 6) + 1) * 6 - 1
    var younger = (Math.floor((base + 1) / 6) + 1) * 6 + 1
    if (ps.every(p => elder % p != 0)) {
      search = false;
      ps.push(elder);
      if (elder > n) return ps;
    }
    if (ps.every(p => younger % p != 0)) {
      search = false;
      ps.push(younger);
    }
    base = base + 6;
  }

  return nextPrimes(n, ps)
}