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           Control.Monad
import qualified Control.Monad.ST            as ST
import qualified Data.ByteString.Char8       as BS
import           Data.List
import           Data.Maybe
import qualified Data.Vector.Unboxed         as V
import qualified Data.Vector.Unboxed.Mutable as VM

readInt = fst . fromJust . BS.readInt
getInt = readInt <$> BS.getLine

primes n = ST.runST $ do
  v <- VM.new (n+1)
  VM.write v 0 (-1)
  VM.write v 1 (-1)
  forM_ [2..n] $ \i -> VM.write v i i
  let sqrtN = ceiling $ sqrt $ fromIntegral n
  forM_ [2..sqrtN] $ \i -> do
    x <- VM.read v i
    when (x >= 0) (forM_ [2..(n`div`i)] $ \j -> VM.write v (i*j) (-1))
  v' <- V.freeze v
  return $ V.filter (> 0) v'

main = do
  x <- getInt
  print $ V.head $ V.dropWhile (< x) $ primes 100003