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 (1.15.1) (judge verdict: Accepted)

//  ____            _                  _                       _       _
// |  _ \ _   _ ___| |_    ___ _ __   | |_ ___ _ __ ___  _ __ | | __ _| |_ ___
// | |_) | | | / __| __|  / __| '_ \  | __/ _ \ '_ ` _ \| '_ \| |/ _` | __/ _ \
// |  _ <| |_| \__ \ |_  | (__| |_) | | ||  __/ | | | | | |_) | | (_| | ||  __/
// |_| \_\\__,_|___/\__|  \___| .__/___\__\___|_| |_| |_| .__/|_|\__,_|\__\___|
//                            |_| |_____|               |_|

//https://github.com/manta1130/Competitive_Programming_Template_Rust

#[macro_use]
mod input {

    use std;
    use std::io;

    const SPLIT_DELIMITER: char = ' ';

    #[macro_export]
    #[allow(unused_macros)]
    macro_rules! input {
    ( $($x:expr ),*) => {
        {
            let temp_str = input_line_str();
            let mut split_result_iter = temp_str.split_whitespace();
                $(
                let buf_split_result = split_result_iter.next();
                let buf_split_result = buf_split_result.unwrap();
                    ($x) = buf_split_result.parse().unwrap();
                )*
        }
    };
}

    #[allow(dead_code)]
    pub fn input_line_str() -> String {
        let mut s = String::new();
        io::stdin().read_line(&mut s).unwrap();
        s.trim().to_string()
    }

    #[allow(dead_code)]
    pub fn p<T>(t: T)
    where
        T: std::fmt::Display,
    {
        println!("{}", t);
    }

    #[allow(dead_code)]
    pub fn input_vector2d<T>(line: usize) -> Vec<Vec<T>>
    where
        T: std::str::FromStr,
    {
        let mut v: Vec<Vec<T>> = Vec::new();

        for _ in 0..line {
            let vec_line = input_vector();
            v.push(vec_line);
        }
        v
    }

    #[allow(dead_code)]
    pub fn input_vector<T>() -> Vec<T>
    where
        T: std::str::FromStr,
    {
        let mut v: Vec<T> = Vec::new();

        let s = input_line_str();
        let split_result = s.split(SPLIT_DELIMITER);
        for z in split_result {
            let buf = match z.parse() {
                Ok(r) => r,
                Err(_) => panic!("Parse Error"),
            };
            v.push(buf);
        }
        v
    }

    #[allow(dead_code)]
    pub fn input_vector_row<T>(n: usize) -> Vec<T>
    where
        T: std::str::FromStr,
    {
        let mut v = Vec::with_capacity(n);
        for _ in 0..n {
            let buf = match input_line_str().parse() {
                Ok(r) => r,
                Err(_) => panic!("Parse Error"),
            };
            v.push(buf);
        }
        v
    }

    pub trait ToCharVec {
        fn to_charvec(&self) -> Vec<char>;
    }

    impl ToCharVec for String {
        fn to_charvec(&self) -> Vec<char> {
            self.to_string().chars().collect::<Vec<_>>()
        }
    }
}

mod vectools {

///C++のupper_boundと同等の実装
pub fn upper_bound<T>(v: &Vec<T>, k: T) -> usize
where
    T: PartialOrd,
{
    let mut from = 0;
    let mut to = v.len();

    while to - from > 1 {
        let mid = (from + to) / 2;
        if v[mid] <= k {
            from = mid;
        } else {
            to = mid;
        }
    }
    if v[from] > k {
        from
    } else {
        to
    }
}

///C++のlower_boundと同等の実装
pub fn lower_bound<T>(v: &Vec<T>, k: T) -> usize
where
    T: PartialOrd,
{
    let mut from = 0;
    let mut to = v.len();

    while to - from > 1 {
        let mid = (from + to) / 2;
        if v[mid] < k {
            from = mid;
        } else {
            to = mid;
        }
    }

    if v[from] < k {
        to
    } else {
        from
    }
}

///次の順列を求める。
pub fn next_permutation<T>(v: &mut Vec<T>) -> bool
where
    T: PartialOrd,
{
    let mut pivot = v.len() - 1;
    loop {
        if pivot == 0 {
            return false;
        }
        if v[pivot] > v[pivot - 1] {
            pivot -= 1;
            break;
        }
        pivot -= 1;
    }
    let mut pivot_swap = v.len() - 1;
    while v[pivot] >= v[pivot_swap] {
        pivot_swap -= 1;
    }
    v.swap(pivot, pivot_swap);
    v[pivot + 1..].reverse();
    true
}

}

use input::*;
use vectools::*;

fn main() {
    let x: usize;
    input!(x);

    let mut prime = vec![];
    let mut table = vec![true; 1000000];
    for i in 2..1000000 {
        if table[i] {
            prime.push(i);
            let mut j = i + i;
            while j < 1000000 {
                table[j] = false;
                j += i;
            }
        }
    }

    let ans = lower_bound(&prime, x);
    p(prime[ans]);
}