Can the execution time of this prime number generator be improved?

Question

My initial goal when writing this was to leave the smallest footprint possible. I can say with confidence that this goal has been met. Unfortunately, this leaves me with a r

Answer 1

I wrote an imperative version, which is faster. It may be impossible to write Sieve of Eratosthenes in a pure functional way to achieve the same speed since you must have a binary state for each number.

let generatePrimes max=
    let p = Array.create (max+1) true
    let rec filter i step = 
        if i <= max then 
            p.[i] <- false
            filter (i+step) step
    {2..int (sqrt (float max))} |> Seq.map (fun i->filter (i+i) i) |> Seq.length |> ignore
    {2..max} |> Seq.filter (fun i->p.[i]) |> Seq.toArray