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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
function eratosthenes3($max) {
	
	// maxの平方根
	$sqrt = floor(sqrt($max));
	
	for ($i=2; $i<=$max; $i++) {
		$lists[$i] = $i;
	}
	
	// もっと単純に倍数を取り除くだけ
	for ($i=2; $i<=$sqrt; $i++) {
		if (isset($lists[$i])) {
			for ($j=$i*2; $j<=$max; $j+=$i) {
				unset($lists[$j]);
			}
		}
	}
	
	return $lists;
}
$prime_lists = eratosthenes3(100003);

$tmp = fgets(STDIN);
foreach ($prime_lists as $key => $value) {
    if($value >= $tmp){
    	$a = $value;
        break;
    }
}
echo $a;