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.*;

public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int x = scanner.nextInt();
        ArrayList<Long> primeNumber = new ArrayList<Long>();
        primeNumber.add(2l);
        long n = 2;
        boolean b = true;
        while (b){
            for(long i = 2;i < n*n;i++){
                if (b){
                    boolean c = true;
                    for (long m:primeNumber){
                        if (i % m == 0){
                            c = false;
                        }
                    }
                    if (c){
                        if (Collections.max(primeNumber)==x){
                            System.out.println(x);
                            b=false;
                        }
                        if (i>x&&b){
                            System.out.println(i);
                            b=false;
                        }
                        primeNumber.add(i);
                    }
                }
            }
            n = n*n;
        }

    }

}