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();
        int n = 100003;
        int[] prime = new int[n - 1];
        for (int i = 0; i < prime.length; i++) {
            prime[i] = 2 + i;
        }
        int k = 0;
        while (prime[k] <= Math.sqrt(n)) {
            if (prime[k] == 0) {
                k++;
                continue;
            }
            for (int i = k + 1; i < prime.length; i++) {
                if (prime[i] % prime[k] == 0) {
                    prime[i] = 0;
                }
            }
            k++;
        }
        for (int i = 0; i < prime.length; i++) {
            if (prime[i] >= x) {
                System.out.println(prime[i]);
                break;
            }
        }
        sc.close();
    }
}