ocaml: phase 5.1 euler7.ml baseline (100th prime = 541)

Scaled-down PE7 (real version asks for the 10001st prime = 104743).
Trial-division within an outer while loop searching forward from 2,
short-circuited via bool ref:

  let nth_prime n =
    let count = ref 0 in
    let i = ref 1 in
    let result = ref 0 in
    while !count < n do
      i := !i + 1;
      let p = ref true in
      let j = ref 2 in
      while !j * !j <= !i && !p do
        if !i mod !j = 0 then p := false;
        j := !j + 1
      done;
      if !p then begin
        count := !count + 1;
        if !count = n then result := !i
      end
    done;
    !result

  nth_prime 100 = 541

100 keeps the run under our 3-minute budget while exercising the
same algorithm.

112 baseline programs total.

lib/ocaml/baseline/euler7.ml

@@ -0,0 +1,22 @@
+let nth_prime n =
+  let count = ref 0 in
+  let i = ref 1 in
+  let result = ref 0 in
+  while !count < n do
+    i := !i + 1;
+    let p = ref true in
+    let j = ref 2 in
+    while !j * !j <= !i && !p do
+      if !i mod !j = 0 then p := false;
+      j := !j + 1
+    done;
+    if !p then begin
+      count := !count + 1;
+      if !count = n then result := !i
+    end
+  done;
+  !result
+
+;;
+
+nth_prime 100

lib/ocaml/baseline/expected.json

@@ -31,6 +31,7 @@
   "euler4_small.ml": 9009,
   "euler5.ml": 232792560,
   "euler6.ml": 25164150,
+  "euler7.ml": 541,
   "euler9.ml": 31875000,
   "expr_eval.ml": 16,
   "expr_simp.ml": 22,

plans/ocaml-on-sx.md

@@ -407,6 +407,11 @@ _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 — 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,
+  short-circuited via bool ref. 100 keeps under 3-min budget while
+  exercising the same algorithm. 112 baseline programs total.
 - 2026-05-09 Phase 5.1 — euler4_small.ml baseline (largest 2-digit
   palindrome product = 9009 = 91 * 99). Scaled-down Project Euler
   #4 (real version uses 3-digit numbers, 906609; that's 810k inner