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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

public class Main {

  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int X = sc.nextInt();
    if (X % 2 == 0 && X != 2) {
      X += 1;
    }
    while (true) {
      boolean A = isPrime(X);
      if (A) {
        System.out.println(X);
        break;
      } else {
        X += 2;
      }
    }
  }

  public static boolean isPrime(int num) {
    if (num < 2)
      return false;
    else if (num == 2)
      return true;
    else if (num % 2 == 0)
      return false; // 偶数はあらかじめ除く

    for (int i = 3; i < num; i += 2) {
      if (num % i == 0) {
        // 素数ではない
        return false;
      }
    }

    // 素数である
    return true;
  }
}