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: Time Limit Exceeded)

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int[] arr = new int[100000 + 2];
        for(int i = 2; i <= (100001 / 2) + 1; i++) {
            for(int j = i + 1; j <= 100001; j++) {
                if(j % i == 0) arr[j] = 1;
            }
        }
        int x = sc.nextInt();
        int ans = 0;
        for(int i = x; i < 100001; i++) {
            if(arr[i] == 0) {
                ans = i;
                break;
            }
        }
        System.out.println(ans);
    }
}