Talk:99 questions/Solutions/31

Does something as simple but as dump as this should be on the wiki ?

isPrime :: Int -> Bool
isPrime n | n <= 1 = False
isPrime n = isPrime' 2 n
    where isPrime' x n | x*x > n   = True
                       | otherwise = (n `rem` x) /= 0 && isPrime' (x+1) n

And something as simple as this one...

isPrime :: Int -> Bool
isPrime n = all (\x -> n `mod`x /= 0) [2..sqr]
	where sqr = floor (sqrt (fromIntegral n :: Double))

-- Assuming that a number is not a prime if he is divisible by any number between 2 and his sqrt

Wilson's theorem

While the square root test is nice and quick, I do believe Wilson's theorem is much more mathematically elegant since it doesn't rely on the knowledge of other primes, even if it is rather slow because of the factorial

fact :: Integer -> Integer
fact n
  | n == 0 = 1
  | otherwise = n * fact (n - 1)

wilsonTest :: Integer -> Bool
wilsonTest p
  | f == (p - 1) = True
  | otherwise    = False
    where f = fact (p - 1) `mod` p

"p is prime iff the product of all positive integers less than p is one less than a multiple of p"