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 Python (3.8.2) (judge verdict: Wrong Answer)

import math
X = int(input())
if X == 2 or X == 3:
    print(X)
    exit()
while True:
    X += 1
    p = True
    for i in range(2, int(math.sqrt(X) + 1)):
        if math.gcd(X, i) > 1:
            p = False
            break
    if p == True:
        print(X)
        exit()