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
X = int(input())
 
if X == 2:
  print(2)
  exit()
  
hajime = X
 
if hajime % 2 == 0:
  hajime += 1
checkMax = math.ceil(math.sqrt(hajime))
for i in range(hajime, 1000000, 2):
  goseisu = False
  for j in range(2, checkMax + 1):
    if i % j == 0:
      goseisu = True
      break
  if not goseisu:
    print(i)
    exit()