let rec seq a b = if a < b then a::(seq (a+1) b) else [b]

let all_primes a b =
let rec sweep m p = function [] -> []
  | head::tail ->
   if m = head then sweep (m+p) p tail
   else head::(sweep (if m < head then m+p else m) p tail) in

 let rec sieve = function [] -> []
  | head::tail -> head::(sieve (sweep head head tail)) in

 sieve (seq a b)

let goldbach n =
 let rec loop2 =
 let rec loop1 m = function [] -> []
  | head::tail -> if n = m+head then [m, head] else loop1 m tail in

 function
  | [] -> raise (Failure "goldbach")
  | head::tail as lst -> match loop1 head lst with
   | [] -> loop2 tail
   | head::_ -> head in

 loop2 (all_primes 2 n)
--------------------------------------------------------------------------------
let goldbach_list a b =
 let rec is_even x =
  if x < 0 then true else if x = 1 then false
  else is_even (x-2) in

 let rec loop = function [] -> []
  | head::tail ->
   if is_even head then (head, goldbach head)::(loop tail)
   else loop tail in

 loop (seq a b)