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<stdlib.h>
#include<stdbool.h>

bool *plfl;

long long lim=3000000;
void sieve_of_erat(){
  plfl=malloc(sizeof(bool)*(lim+5));
  long long i,j;
  for(i=0;i<lim+5;i++){plfl[i]=true;}
  plfl[0]=false;
  plfl[1]=false;
  for(i=2;i<lim;i++){
    if(!plfl[i]){continue;}
    for(j=2*i;j<lim;j+=i){
      plfl[j]=false;
    }
  }
  return;
}

int main(){
  sieve_of_erat();
  long long i,r=0,x;
  scanf("%lld",&x);
  for(i=x;i<2000000;i++){
    if(plfl[i]){printf("%lld\n",i);return 0;}
  }
  return 0;
}