after looking at the pseudocode for the Sieve of Eratosthenes on wikipedia I tried implementing a similar version using F#. The code runs just fine, that is, it returns all prime numbers up until a given number. But I was wondering if the implementation could be improved. See below for the code:

let rec sieve xs count maxNumb = 
    match count = maxNumb with
    | true -> xs
    | false when (Array.contains count xs) -> 
        |> Array.filter (fun ys -> ys % count <> 0. || ys = count)
        |> fun filteredArr -> sieve filteredArr (count + 1.) maxNumb
    | false -> sieve xs (count + 1.) maxNumb

let findPrimes maxNumb = 
    sieve [|2. .. maxNumb|] 2. maxNumb
findPrimes 30.

[|2.0; 3.0; 5.0; 7.0; 11.0; 13.0; 17.0; 19.0; 23.0; 29.0|]

Thank you in advance for any comments or remarks :)

  • 2
    \$\begingroup\$ You might be interested in Melissa O'Neill's paper The Genuine Sieve of Eratosthenes which explains how the classic Haskell one-liner is, in fact, not actually the Sieve of Eratosthenes, what – in her opinion – are the important traits of what makes program a "genuine" implementation of the Sieve of Eratosthenes, then shows a lazy, purely functional implementation of an algorithm that does exhibit the traits she defined as "genuine". While the laziness part is not directly applicable to F#, the rest is. \$\endgroup\$ Jan 1, 2022 at 11:22
  • \$\begingroup\$ Thank you so much Jörg W Mittag! I just had a look at the paper, I will definitely come back with a better implementation. :) \$\endgroup\$ Jan 3, 2022 at 2:00

1 Answer 1


One small improvement. You can remove one of the recursive calles which improves readability and enables the compiler to use tail recursion:

let rec sieve xs count maxNumb =        
    if count = maxNumb then xs
        let xs' = if xs |> Array.contains count 
                  then xs |> Array.filter (fun ys -> ys % count <> 0. || ys = count)
                  else xs
        sieve xs' (count + 1.) maxNumb    

Further more, I was wondering why not using a list instead of the array because lists are more "functional-like". Comparing the performance of list usage vs. array usage, the array was 10 times faster ^^.


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