gistfile1.fs

(*
  Problem 3
    The prime factors of 13195 are 5, 7, 13 and 29.
    What is the largest prime factor of the number 600851475143 ?
*)
let rec find_factors (count, target, list) =
  if count < 2L then (1L,target,count::list)
  else if (target % count = 0L) then find_factors((count-1L), target, count::list)
  else find_factors((count-1L),target, list)

let rec is_prime number = 
  let _,_,list = find_factors (number,number,[])
  let output = List.fold (+) 0L list
  (output = (number + 1L))

let _,_,factors = find_factors (600851475143L,600851475143L,[])
factors
  |> List.rev
  |> List.filter (fun n -> (n%2L) > 0L || (n%5L) > 0L)
  |> List.filter (fun n -> is_prime n)