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)

#![allow(non_snake_case)]
#![allow(unused_imports)]
use proconio::input;
use std::cmp::max;
use std::cmp::min;
use std::collections::HashMap;
use std::collections::VecDeque;

// Sieve of Eratosthenes
fn get_primes(input: i64) -> Vec<i64> {
    let N: usize = max(input, 100) as usize;

    let mut Alive = vec![true; N];
    Alive[0] = false;
    Alive[1] = false;

    // i番目の素数が分かる (0-origin)
    let mut Ps: Vec<i64> = Vec::new();

    for smallest in 2..=((N as f64).sqrt()) as usize + 1 {
        if !Alive[smallest] {
            continue;
        }

        for i in (smallest * 2..N).step_by(smallest) {
            Alive[i] = false;
        }
    }

    for i in 2..N {
        if Alive[i] {
            Ps.push(i as i64);
        }
    }

    return Ps;
}

fn main() {
    input! {
        X: i64,
    }

    let primes = get_primes(100004);

    for &p in primes.iter() {
        if p >= X {
            println!("{}", p);
            return;
        }
    }
}