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: Accepted)

import sys
from collections import deque
#import numpy as np
import math
#sys.setrecursionlimit(10**6)
def S(): return sys.stdin.readline().rstrip()
def SL(): return map(str,sys.stdin.readline().rstrip().split())
def I(): return int(sys.stdin.readline().rstrip())
def IL(): return map(int,sys.stdin.readline().rstrip().split())

def solve():
    exclude = set()
    prime = set()
    for i in range(2,int(math.sqrt(x))+1):
        if i in exclude:
            continue
        prime.add(i)
        j = i
        while j<=x+2*i:
            exclude.add(j)
            j += i
    current = x
    while True:
        for rep in prime:
            if current%rep==0:
                break
        else:
            print(current)
            return
        current += 1
    return

if __name__=='__main__':
    x = I()
    solve()