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 Rust (1.42.0) (judge verdict: Accepted)

fn main() {
    proconio::input! {
        x: usize,
    }
    let n=x*2;
    let mut p=vec![true;n];
    let mut i=2;
    while i*i<=n {
        if p[i] {
            let mut k=2;
            while i*k<n {
                p[i*k]=false;
                k+=1;
            }
        }
        i+=1;
    }
    for i in x..n {
        if p[i] {
            println!("{}",i);
            break;
        }
    }
}