{-# LANGUAGE BangPatterns #-} import Control.Monad import Data.Bits import Data.Bool import qualified Data.List as L import qualified Data.Array.ST as ArrST import qualified Data.Array.Unboxed as ArrU import qualified GHC.Integer.GMP.Internals as GMP infixl 8 .<<., .>>. (.<<.) :: Bits b => b -> Int -> b (.<<.) = unsafeShiftL {-# INLINE (.<<.) #-} (.>>.) :: Bits b => b -> Int -> b (.>>.) = unsafeShiftR {-# INLINE (.>>.) #-} fi :: Int -> Integer fi = fromIntegral {-# INLINE fi #-} fI :: Integer -> Int fI = fromInteger {-# INLINE fI #-} ctz :: FiniteBits fb => fb -> Int ctz = countTrailingZeros {-# INLINE ctz #-} millerRabin :: Int -> Bool millerRabin k | k <= 3 = k == 2 || k == 3 | even k = False | otherwise = mr k where mr :: Int -> Bool mr n | n < 2047 = loop [2] | n < 1373653 = loop [2,3] | n < 9080191 = loop [31,73] | n < 25326001 = loop [2,3,5] | n < 4759123141 = loop [2,7,61] | n < 1122004669633 = loop [2,13,23,1662803] | n < 2152302898747 = loop [2,3,5,7,11] | n < 3474749660383 = loop [2,3,5,7,11,13] | n < 341550071728321 = loop [2,3,5,7,11,13,17] | otherwise = loop [2,325,9375,28178,450775,9780504,1795265022] where powModInt :: Int -> Int -> Int -> Int powModInt !a !n !mo = fI $ GMP.powModInteger (fi a) (fi n) (fi mo) !m = n - 1 !s = ctz m !d = m .>>. s loop :: [Int] -> Bool loop [] = True loop (a:as) | powModInt a d n /= 1 && allok = False | otherwise = loop as where allok = all (\r -> (powModInt a ((1 .<<. r) * d) n) /= m) $ [0..(s - 1)] main :: IO () main = do n <- readLn :: IO Int print $ bool (n + 100) (n + 99) (millerRabin (n + 100))