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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Data.List
import Data.Maybe

main = print =<< sol <$> readLn

sol x = fromJust $ find (>=x) primes 

primes :: Integral a => [a]
primes = 2 : filter ((==1) . length . primeFactors) [3,5..]

primeFactors :: Integral a => a -> [a]
primeFactors 1 = []
primeFactors n = factor n primes

factor :: Integral a => a -> [a] -> [a]
factor n (p:ps) 
  | p*p > n        = [n]
  | n `mod` p == 0 = p : factor (n `div` p) (p:ps)
  | otherwise      = factor n ps