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 (3.4.3) (judge verdict: Accepted)

import sys

input = sys.stdin.readline

ri = lambda: int(input())
rs = lambda: input().rstrip()
ril = lambda: list(map(int, input().split()))
rsl = lambda: input().rstrip().split()
ris = lambda n: [ri() for _ in range(n)]
rss = lambda n: [rs() for _ in range(n)]
rils = lambda n: [ril() for _ in range(n)]
rsls = lambda n: [rsl() for _ in range(n)]


def eratosthenes(n):
    sieve = [True for _ in range(n + 1)]
    sieve[0] = False
    sieve[1] = False

    def _update(p):
        if sieve[p]:
            for i in range(p * 2, n + 1, p):
                sieve[i] = False

    if n > 1:
        _update(2)
    p = 3
    while p * p <= n:
        _update(p)
        p += 2
    return sieve


x = ri()

sieve = eratosthenes(10**6)
for i in range(x, 10**6):
    if sieve[i]:
        print(i)
        exit()