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)

# coding: utf-8
 
def is_prime2(q,k=100):
  q = abs(q)
  if q == 2: return True
  if q < 2 or q&1 == 0: return False
  for i in range(3,k):
    x,y = q,i
    while y:
      x, y =  y, x % y
    if x != 1: continue
    if pow(i, q-1, q) != 1:
      return False
  return True
 
X = int(input())
 
for i in range(X,10**5+4):
  if is_prime2(i):
    print(i)
    exit()