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();
    boolean[] prime = new boolean[200001];
    for(int i = 2; i < 200001; i++) {
      prime[i] = true;
    }
    prime[1] = false;
    for(int i = 2; i < 200001; i++) {
      if(prime[i]) {
        for(int j = (2 * i); j < 200001; j += i) {
          prime[j] = false;
        }
      } 
    }
    int ans = 0;
    for(int i = 2; i < 200001; i++) {
      if((prime[i]) && (i >= x)) {
        ans = i;
        break;
      }
    }
    System.out.println(ans);
  }
}