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: Accepted)

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

#define MAX 200000

int prime[MAX + 1];

int main(){
  int x;
  int limit;
  int i,j;

  scanf("%d", &x);

  for(i = 2;i <= MAX;i++) prime[i] = 1;
  limit = sqrt(MAX);

  for(i = 2;i <= limit;i++){
    if(prime[i] == 1){
      for(j = i*2;j <= MAX;j++){
        if(j % i == 0) prime[j] = 0;
      }
    }
  }

  while(prime[x] != 1) x++;

  printf("%d\n", x);

  return 0;
}