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 math

def is_sosuu(X):
  # 2以外の偶数は素数ではないので無視する
  if X % 2 == 0 and N != 2:
    return False
  
  # 繰り返しの上限を対象の平方根にする
  limit = int(math.sqrt(X)) + 1
  # ２の倍数を省く
  numbers = [i for i in range(3, limit) if i % 2 == 1]
  for i in numbers:
    if X % i == 0:
      return False

  return True

N = int(input())
while True:
  if is_sosuu(N):
    print(N)
    break
  N+=1