ocaml: phase 5.1 prime_factors.ml baseline (trial-division, 360 factor sum = 17)

Three refs threading through a while loop:
  m       remaining quotient
  d       current divisor
  result  accumulator (built in reverse, List.rev at end)

  while !m > 1 do
    if !m mod !d = 0 then begin
      result := !d :: !result;
      m := !m / !d
    end else
      d := !d + 1
  done

360 = 2^3 * 3^2 * 5 factors to [2;2;2;3;3;5], sum 17.

60 baseline programs total — milestone.

lib/ocaml/baseline/expected.json

@@ -46,6 +46,7 @@
   "pi_leibniz.ml": 314,
   "pretty_table.ml": 64,
   "poly_stack.ml": 5,
+  "prime_factors.ml": 17,
   "queens.ml": 2,
   "quicksort.ml": 44,
   "roman.ml": 44,

lib/ocaml/baseline/prime_factors.ml

@@ -0,0 +1,16 @@
+let factor n =
+  let result = ref [] in
+  let m = ref n in
+  let d = ref 2 in
+  while !m > 1 do
+    if !m mod !d = 0 then begin
+      result := !d :: !result;
+      m := !m / !d
+    end else
+      d := !d + 1
+  done;
+  List.rev !result
+
+;;
+
+List.fold_left (+) 0 (factor 360)

plans/ocaml-on-sx.md

@@ -407,6 +407,12 @@ _Newest first._
   binary search tree (`type 'a tree = Leaf | Node of 'a * 'a tree *
   'a tree`) with insert + in-order traversal. Tests parametric ADT,
   recursive match, List.append, List.fold_left.
+- 2026-05-09 Phase 5.1 — prime_factors.ml baseline (trial-division
+  factorisation, sum of factors of 360 = 17). Three refs threading
+  through a while loop: m holds the remaining quotient, d the
+  current divisor, result accumulates factors. When `m mod d = 0`,
+  push d and divide; otherwise increment d. 360 = 2^3 * 3^2 * 5
+  factors to [2;2;2;3;3;5], sum 17. 60 baseline programs total.
 - 2026-05-09 Phase 5.1 — atm.ml baseline (mutable record + custom
   exception + try/with, balance 120 after rollback). Models a bank
   account: deposit/withdraw mutate the balance field; an over-draw