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: Runtime Error)


import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int x = sc.nextInt();

		int max_size = 1000000020 + 1;
		boolean[] list = new boolean[max_size];
		for(int i = 0; i < max_size; i++) {
			list[i] = true;
		}
		
		
		// エラトステネスの篩を作る
		int root_max = (int) Math.sqrt(max_size) + 1;
		for(int i = 2; i < root_max; i++) {
			// list[i] == trueなら、素数
			if(list[i]) {
				// 倍数だけをfalseにする
				for(int j = i * 2; j < max_size; j+=i) {
					list[j] = false;
				}
			}
		}

		//System.out.println(list[x]);
		while(true) {
			if(list[x]) {
				System.out.println(x);
				break;
			}
			x++;
		}

	}
}