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 <math.h>


int main(void){

    int X = 0;
    int d_X = 0.0;
    int flag = 0;
    int i = 0;

    scanf("%d", &X);

    while (flag == 0){

        d_X = sqrt((double)X);

        if (X == 2){
            flag = 1;

        } else {

            if (X % 2 == 0){
                X++;

            } else {

                for (i = 3; i <= (int)d_X; i = i + 2){
                    //printf("%d\n", i);
                    //printf("%d\n", X);
                    //printf("%d\n", X % i);


                    if (X % i == 0){
                        X++;
                        break;

                    } 
                }
                if (i >= (int)d_X){
                    flag = 1;
                }   
            }
        }
    }
    printf("%d", X);

    return 0;
}