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 Scala (2.11.7) (judge verdict: Time Limit Exceeded)

object Main extends App {
  import io.StdIn._
  val x = readLine().toInt
  var primesUnderX: List[Int] = List.empty
  for (i <- 2 to x - 1) {
    if (!primesUnderX.exists(p => i % p == 0)) {
      primesUnderX = i :: primesUnderX
    }
  }
  var ans = x
  while (primesUnderX.exists(p => ans % p == 0)) {
    ans += 1
  }

  println(ans)
}