F#. Terminated due to timeout when solving Project Euler #3 problem - algorithm

Question

I told about that problem: https://www.hackerrank.com/contests/projecteuler/challenges/euler003
I am trying to solve this problem as follows:
open System
let isPrime n =
match n with
| _ when n > 3L && (n % 2L = 0L || n % 3L = 0L) -> false
| _ ->
let maxDiv = int64(System.Math.Sqrt(float n)) + 1L
let rec f d i =
if d > maxDiv then
true
else
if n % d = 0L then
false
else
f (d + i) (6L - i)
f 5L 2L
let primeFactors n =
let rec getFactor num proposed acc =
match proposed with
| _ when proposed = num -> proposed::acc
| _ when num % proposed = 0L -> getFactor (num / proposed) proposed (proposed::acc)
| _ when isPrime num -> num::acc
| _ -> getFactor num (proposed + 1L) acc
getFactor n 2L []
let pe3() =
for i = 1 to Console.ReadLine() |> int do
let num = Console.ReadLine() |> int64
let start = DateTime.Now
primeFactors num
|> List.max
|> printfn "%i"
let elapsed = DateTime.Now - start
printfn "elapsed: %A" elapsed
pe3()
There are results of my testing:
Input: 10 Output: 5 Elapsed time: 00:00:00.0562321
Input: 123456789 Output: 3803 Elapsed time: 00:00:00.0979232
Input: 12345678999 Output: 1371742111 Elapsed time: 00:00:00.0520280
Input: 987654321852 Output: 680202701 Elapsed time: 00:00:00.0564059
Input: 13652478965478 Output: 2275413160913 Elapsed time:
00:00:00.0593369
Input: 99999999999999 Output: 909091 Elapsed time: 00:00:00.1260673
But I anyway get Terminated due to timeout in Test Case 5. What can I do?

Answer 1

There is a solution:
open System
let primeFactors n =
let rec getFactor num proposed acc =
match proposed with
| _ when proposed*proposed > num -> num::acc
| _ when num % proposed = 0L -> getFactor (num / proposed) proposed (proposed::acc)
| _ -> getFactor num (proposed + 1L) acc
getFactor n 2L []
let pe3() =
for i = 1 to Console.ReadLine() |> int do
printfn "%i" (primeFactors (Console.ReadLine() |> int64)).Head
pe3()
Thanks Will Ness and rici.

Answer 2

There is no need to write super sophisticated code for this challenge. A simple algorithm to enumerate a number's prime factors will do the trick. My code creates a seq of the prime factors, then finds the maximum, and prints it. The rest of the code shows a nice functional way of handling processing of lines read from standard input.
module Auxiliaries =
let isNull (x : 'a when 'a : not struct) =
match box x with
| null -> true
| _ -> false
let refAsOption x =
if isNull x then None else Some x
let readLinesFromTextReader r =
let tryRdLn (r : System.IO.TextReader) =
try refAsOption (r.ReadLine ()) with _ -> None
let gen r =
tryRdLn r |> Option.map (fun s -> (s, r))
Seq.unfold gen r
module Contest =
let factors num =
let next n =
if n = 2L then 3L
elif n % 6L = 1L then n + 4L
else n + 2L
let rec loop nn ct lf =
seq {
if ct * ct > nn then
if nn > lf then yield nn
elif nn % ct = 0L then
yield ct
yield! loop (nn / ct) ct ct
else
yield! loop nn (next ct) lf
}
loop num 2L 0L
let euler003 n = factors n |> Seq.max
let () =
Auxiliaries.readLinesFromTextReader stdin
|> Seq.skip 1
|> Seq.map (int64 >> euler003)
|> Seq.iter stdout.WriteLine