Prime number check

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

Can you flesh out your question to explain how you call `isPrime` initially (i.e. what the initial value of `iterator` is), and give an example of a wrong result it gives. Also, how can the code you've written ever return `true`? — Ganesh Sittampalam, Nov 02 '14 at 16:09
The second case should evaluate to `true` instead of recursing further.. That was the error, thanks for helping me find it! — Overly Excessive, Nov 02 '14 at 16:12

score 3 · Accepted Answer · answered Nov 02 '14 at 16:50

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

Oh a nested recursive function, that is just genius! I was looking for a way to do optional parameters in F# to achieve the same thing, but a nested recursion is much smarter! The reason I have steered clear of using an `if` statement is that I read that using the use of pattern match is more idiomatic in F# but as you can tell I am completely new to F# so I might've misread or misunderstood :). — Overly Excessive, Nov 02 '14 at 18:13

Prime number check

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