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

main :: IO ()
main = do
  l1 <- getLine
  let x = read l1 :: Int
  print $ head $ dropWhile (<x) primes

primes :: [Int]
primes = primes' [2..]

primes' :: [Int] -> [Int]
primes' (p:l) = ps' ++ primes' l''
  where (ps, l') = span (<p*p) l
        ps' = p:ps
        l'' = filter (\x -> all (\p -> x `mod` p /= 0) ps') l'