From c16a8f2d53bf9362609a7d80d81bacbe34c3f5f1 Mon Sep 17 00:00:00 2001
From: giles <giles.bradshaw@rose-ash.com>
Date: Sat, 9 May 2026 21:16:40 +0000
Subject: [PATCH] ocaml: phase 5.1 is_prime.ml baseline (count primes <= 100 =
 25)
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Trial division up to sqrt(n) with early-exit via bool ref:

  let is_prime n =
    if n < 2 then false
    else
      let p = ref true in
      let i = ref 2 in
      while !i * !i <= n && !p do
        if n mod !i = 0 then p := false;
        i := !i + 1
      done;
      !p

Outer count_primes loops 2..n calling is_prime, accumulating count.
Returns 25 — the canonical prime-counting function pi(100).

107 baseline programs total.
---
 lib/ocaml/baseline/expected.json |  1 +
 lib/ocaml/baseline/is_prime.ml   | 21 +++++++++++++++++++++
 plans/ocaml-on-sx.md             |  6 ++++++
 3 files changed, 28 insertions(+)
 create mode 100644 lib/ocaml/baseline/is_prime.ml

diff --git a/lib/ocaml/baseline/expected.json b/lib/ocaml/baseline/expected.json
index 7613a491..862e864c 100644
--- a/lib/ocaml/baseline/expected.json
+++ b/lib/ocaml/baseline/expected.json
@@ -46,6 +46,7 @@
   "hanoi.ml": 1023,
   "hist.ml": 75,
   "int_sqrt.ml": 1027,
+  "is_prime.ml": 25,
   "fizz_classifier.ml": 540,
   "fizzbuzz.ml": 57,
   "flatten_tree.ml": 28,
diff --git a/lib/ocaml/baseline/is_prime.ml b/lib/ocaml/baseline/is_prime.ml
new file mode 100644
index 00000000..8e97fb0f
--- /dev/null
+++ b/lib/ocaml/baseline/is_prime.ml
@@ -0,0 +1,21 @@
+let is_prime n =
+  if n < 2 then false
+  else
+    let p = ref true in
+    let i = ref 2 in
+    while !i * !i <= n && !p do
+      if n mod !i = 0 then p := false;
+      i := !i + 1
+    done;
+    !p
+
+let count_primes n =
+  let c = ref 0 in
+  for i = 2 to n do
+    if is_prime i then c := !c + 1
+  done;
+  !c
+
+;;
+
+count_primes 100
diff --git a/plans/ocaml-on-sx.md b/plans/ocaml-on-sx.md
index e9809c3a..56749bed 100644
--- a/plans/ocaml-on-sx.md
+++ b/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 — is_prime.ml baseline (count primes ≤ 100 =
+  25). Trial division up to √n with early-exit via bool ref. Loop
+  2..n calling is_prime, accumulate count. Returns 25 (the canonical
+  prime-counting function π(100)). Tests two cooperating functions
+  + while-with-bool-short-circuit + nested for. 107 baseline
+  programs total.
 - 2026-05-09 Phase 5.1 — catalan.ml baseline (Catalan number C(5)
   via DP recurrence = 42). DP recurrence `C(n) = sum_{j=0}^{n-1}
   C(j) * C(n-1-j)`. C(5) = 42 — also the count of distinct binary