Demo — parallel prime count / find

• Type: feature — example app. Track B/E (build with $(PXX_STABLE); a compiler/frontend gap it hits → file under the owning lane).
• Opened: 2026-07-17 (parallel-demo candidate).
• Relation: integer companion to examples/parallel/collatz.pas (uneven load) and membw.pas (memory-bound). Uses parallel(P) for + reduction ([[feature-parallel-for-scheduling-policy]]). There is already a serial examples/primes/sieve.pas to reuse / contrast.

Goal

The cleanest EVEN-LOAD integer showcase: count primes in [2..N].

var primes: Int64;
primes := 0;
parallel(pdChunked) for n := 2 to N reduction(+: primes) do
  if IsPrime(n) then primes := primes + 1;

IsPrime is a function (trial division up to sqrt(n)) → its scratch is private on the worker stack, result folds into the reduction var (the safe pattern). Pure integer, deterministic (serial == parallel), embarrassingly parallel.

Contrast with Collatz: prime trial-division cost grows smoothly with n (roughly sqrt(n)), so contiguous pdChunked is already fairly balanced — a good foil to Collatz where the cost is erratic. Optionally also time pdOnDemand to show it's ~equal here (distribution matters only for erratic loads).

Phases / extensions

1. Count (above) — serial vs parallel timing + reduction agreement.
2. Segmented sieve — a memory + integer variant: sieve [lo..hi] blocks in parallel (each worker owns a disjoint segment, sieves with the base primes), count set bits. Closer to how real prime enumeration scales; touches the memory side too.
3. Find the largest prime gap in the range via reduction(max: gap) — shows a second reduction op on the same pass.

Constraints

• Build with $(PXX_STABLE); never rebuild the compiler.
• No automated multithread test without explicit permission (core-pegging) — manual-validation, compile-smoke at most. A single-threaded correctness check (count matches a known π(N)) is fine to automate and bounded.

Acceptance

• A prime-count demo: serial vs parallel timing, reduction(+) total, asserts parallel == serial and matches the known prime count for the chosen N (e.g. π(10^7) = 620,458). Compiles + runs on x86-64; compiles cross.

Log

• 2026-07-17 — Filed as a parallel-demo candidate (even-load integer foil to Collatz; segmented-sieve extension for the memory angle).
• 2026-07-20 — resolved, commit HEAD.