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# Prime Grokking
**Can a minimal architecture learn the next-prime function — or *grok* it rather than memorize it?**
The grokking literature studies almost exclusively group-structured tasks (modular arithmetic).
Next-prime supplies the missing **non-group-structured case**. Results so far (phases 1–4,
range [2, 100]): **no grokking observed** — memorization, partial in-range generalization, and a
decomposition surprise (is-prime generalizes ~2.5x better than next-prime), but no delayed
transition. That negative-class result is the point of the project; E6 (range [2, 1000]) and a
long-horizon follow-up are in flight.
**The unusual bit:** every batch is **pre-registered**. Before each run, the outcome →
interpretation matrix is committed to the private research repo (the commit hash is the lock),
and results are interpreted *only* against that lock. The complete record, addenda 1–6, is
mirrored in [`design/preregistration.md`](design/preregistration.md).
## Contents
- `design/` — experiment spec, full pre-registration, external review passes (Gemini, Codex) including rejected points and why
- `src/` — config, data (sieve + bisect), weight-tied ACT-GRU RNN, GPT-style transformer baseline, train, eval (chunked, probe reports)
- `tests/` — 48-test pytest suite (data correctness, weight-tying, batch invariance, device handling, scaling)
- `scripts/` — idempotent sweep runner, experiment launcher, plots
- `NOTES-*.md` — per-phase analyses written against the lock, not after the fact
- `runs/*/summary.csv` — headline numbers per phase (raw run dirs are gitignored; everything is regenerable)
## Quick start
CPU (no GPU needed, ~35 min/run on 2 cores):
```bash
python3 -m venv .venv
.venv/bin/pip install torch --index-url https://download.pytorch.org/whl/cpu
.venv/bin/pip install numpy matplotlib pytest
.venv/bin/pytest tests/ -q
.venv/bin/python -m src.train rnn 0
```
CUDA (AMP fp16 is on by default on CUDA; Turing tensor cores):
```bash
.venv/bin/pip install torch --index-url https://download.pytorch.org/whl/cu126
.venv/bin/python -m src.train transformer 0 --range_end 1000 --max_steps 32 --device cuda
```
Notes: `--max_steps` is K (the tied-iteration cap — it must exceed the max prime gap of the
range: 20 below 1000, 36 below 10^4, 72 below 10^5). `--compile_model True` roughly doubles the
transformer on CUDA but hurts the RNN (dynamic halting breaks graph capture). Full flag surface
(weight decay, train fraction, task mode, vocab mode, halting ablation, cosine decay) lives in
`src/config.py`.
## Research discipline
- Outcome (O1–O4), probe-signature (P1–P6), and halting (H1–H4) codes locked before runs; no post-hoc reinterpretation — `NOTES-*.md` compares measurements against the lock and reports whichever branch fired.
- Seed replication for headline cells; no hyperparameter tuning on the validation split.
- Pre-registered interpretation matrices were reviewed by external models (Gemini, Codex) before locking.
## Blog
The experiment is covered in a multi-part series on [jayrup.me](https://jayrup.me/) (parts 1–3, Aug 2026).
## License
[MIT](LICENSE)
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