(*
It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.
9 = 7 + 2×1^(2)
 15 = 7 + 2×2^(2)
 21 = 3 + 2×3^(2)
 25 = 7 + 2×3^(2)
 27 = 19 + 2×2^(2)
 33 = 31 + 2×1^(2)
It turns out that the conjecture was false.
What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?
*)

let goldbach =
  (* whether x is a sum of y*y and a prime from ps *)
  let rec is_goldbach x ps y =
    ( y<x ) && 
    ( ( List.exists (fun p-> x = p+2*y*y) ps ) ||
      ( is_goldbach x ps (y+1) ) )
  in
  let rec goldbach x ps =
    Printf.printf "%d\n" x;
    if( List.exists (fun y->x mod y=0) ps)
    then
      if (( x mod 2 = 0) || (is_goldbach x ps 0))
      then goldbach (x+2) ps
      else x
    else
      goldbach (x+2) (x::ps)
  in
    goldbach 3 [2]
;;

Printf.printf "%d\n" goldbach;;