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 <time.h>
#include <math.h>
int era(int x,int *prime);
int main(){
    long int x;
    scanf("%ld",&x);
    int *a=(int*)malloc(sizeof(int)*(x-2));
    int c=0;
    int l=era(x-1,a);
    for(int i=x;;i++){
        c=0;
        for(int j=0;j<l;j++){
            if(i%a[j]==0){
                c=1;
                break;
            }
        }
        if(c==0){
            printf("%d\n",i);
            break;
        }
    }
    free(a);
    return 0;
}

int era(int x,int *prime){
    int i, j= 0;
    int count = 0;
    int *flags = (int*)calloc(x+1,sizeof(int));
    for (i = 2; i <= x; i++) {
        if (flags[i] == 0) {
            ++count;
            prime[count-1]=i;
            for (j = i * 2; j <= x; j += i) {
                flags[j] = 1;
            }
        }
    }
    return count;
}