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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <string.h>
#include <math.h>
#include <stdlib.h>

int main(void){
  long x;
  scanf("%ld", &x);
  long k = 3;

  if(x<=1) return -1;
  if(x == 2){
    printf("2\n");
    return 0;
  }

  if(x%2 == 0)
    x++;
  while(1){
    while(x%k)
      k += 2;
    if(k == x){
      printf("%ld\n", x);
      return 0;
    }
    else
      x+=2;
  }    
}