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 = do
  x <- readLn :: IO Integer
  putStrLn $ show $ head $ filter (>= x) $ primes

primes :: [Integer]
primes = 2 : [ n | n <- [3..], head (primeFactors n) == n ]

primeFactors :: Integer -> [Integer]
primeFactors n = factors n primes
    where factors n ps@(p:qs)
              | n < 2        = []
              | n < p^2      = [n]
              | mod n p == 0 = p : factors (div n p) ps
              | otherwise    = factors n qs