素数检查

Question

I'm having some issues with my prime number checker in F#. It doesn't seem to give the right results so I'm guessing I've screwed up the logic somewhere but I can't figure out where. The implementation is a simple brute forcing one so the logic isn't complicated and I've implemented similiar solutions using for loops in imperative languages before.

let rec isPrime iterator (n : int) = 
                            match iterator with
                            | 1 -> isPrime (iterator + 1) n
                            | a when a = n -> isPrime (iterator + 1) n
                            | _ -> match n % iterator = 0 with
                                    | true -> false
                                    | false -> isPrime (iterator + 1) n

Answer 1

As you already figured out in the comments, the problem is that the function should terminate and say true when the iterator reaches n . You can actually make it faster just by iterating up to square root of n or at least n/2 because by the time you reach n/2 , you know it will be a prime.

This kind of logic seems to be easier to write using if rather than match - although you can easily fix it by fixing the case in match , I'd probably write something like:

let rec isPrime iterator (n : int) = 
  if iterator = n / 2 then true
  elif iterator = 1 then isPrime (iterator + 1) n
  elif n % iterator = 0 then false
  else isPrime (iterator + 1) n

Also, you might not want to expose the iterator parameter to the user - you can write the code using a nested function which calls the loop starting with iterator = 2 (and then you don't need the iterator = 1 case at all):

let isPrime (n : int) = 
  let rec loop iterator = 
    if iterator = n/2 then true
    elif n % iterator = 0 then false
    else loop (iterator + 1)
  loop 2