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)

X = int(input())
def eratosthenes(N):
  s = [i % 2 for i in range(N)]
  s[0] = s[1] = 0
  s[2] = 1

  for i in range(2, int(N**0.5)):
    if s[i] == 0: continue
    for j in range(2 * i, N, i):
      s[j] = 0
  
  return s

s = eratosthenes(10**5 + 10)
for i in range(X, 10**5+10):
  if s[i] == 1:
    print(i)
    break