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let prec = 1_000_000
let max_n = 205_211
let to_string = Gmp.F.to_string_base_digits ~base:10 ~digits:0

let euler_fraction n =
  let open Z in
  let numerator = ref one in
  let denominator = ref one in
  for i = 1 to n do
    numerator := succ (!numerator * (of_int i));
    denominator := (of_int i) * !denominator;
  done;
  (!numerator, !denominator)

let f () =
  let (num, den) = euler_fraction max_n in
  let znum = Gmp.F.from_string (Z.to_string num) in
  let zden = Gmp.F.from_string (Z.to_string den) in
  let euler = Gmp.F.div_prec ~prec znum zden in
  print_endline @@ to_string euler

let () = f ()