ocaml: phase 5.1 euler3.ml baseline (largest prime factor of 13195 = 29)

PE3's worked example. Trial-division streaming: when the current
factor divides m, divide and update largest; otherwise bump factor:

  let largest_prime_factor n =
    let m = ref n in
    let factor = ref 2 in
    let largest = ref 0 in
    while !m > 1 do
      if !m mod !factor = 0 then begin
        largest := !factor;
        m := !m / !factor
      end else factor := !factor + 1
    done;
    !largest

  largest_prime_factor 13195 = 29  (= 5 * 7 * 13 * 29)

The full PE3 number 600851475143 exceeds JS safe-int (2^53 ≈ 9e15
in float terms; 6e11 is fine but the intermediate 'i mod !factor'
on the way to 6857 can overflow precision). 13195 keeps the program
portable across hosts.

113 baseline programs total.

lib/ocaml/baseline/euler3.ml

@@ -0,0 +1,15 @@
+let largest_prime_factor n =
+  let m = ref n in
+  let factor = ref 2 in
+  let largest = ref 0 in
+  while !m > 1 do
+    if !m mod !factor = 0 then begin
+      largest := !factor;
+      m := !m / !factor
+    end else factor := !factor + 1
+  done;
+  !largest
+
+;;
+
+largest_prime_factor 13195

lib/ocaml/baseline/expected.json

@@ -28,6 +28,7 @@
   "euler1.ml": 233168,
   "euler10.ml": 1060,
   "euler2.ml": 4613732,
+  "euler3.ml": 29,
   "euler4_small.ml": 9009,
   "euler5.ml": 232792560,
   "euler6.ml": 25164150,

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 — euler3.ml baseline (largest prime factor of
+  13195 = 29; PE3's worked example). Trial-division streaming: when
+  the current factor divides m, divide and update largest; otherwise
+  bump factor. Numbers like 600851475143 (the actual PE3) exceed JS
+  safe-int (2^53 ≈ 9e15), so 13195 keeps the program portable. 113
+  baseline programs total.
 - 2026-05-09 Phase 5.1 — euler7.ml baseline (100th prime = 541;
   scaled-down PE7 which asks for the 10001st = 104743). Trial-
   division within an outer while loop searching forward from 2,