# E015: Wilson test infeasibility

```{figure} ../_static/experiments/e015_hero.png
:width: 80%
:alt: Preview figure for E015
```

**Tags:** `number-theory`, `quantitative-exploration`, `visualization`
See: {doc}`../tags`.

## Highlights

- This is a thin wrapper that follows the standard experiment template and delegates the actual computation to :mod:`mathxlab.experiments.prime_suite`.
- Writes reproducible artifacts (`params.json`, `report.md`, and figures).
- Designed to surface patterns *and* “looks-true-until-it-breaks” behavior.

## Goal

This is a thin wrapper that follows the standard experiment template and delegates the actual computation to :mod:`mathxlab.experiments.prime_suite`.

## Background (quick refresher)

- {doc}`../background/prime-numbers`

## Research question

Which **prime-related claim, heuristic, or algorithm** breaks first under a clean, controlled computational sweep,
and what does the smallest or clearest counterexample (or deviation) look like?

## Why this qualifies as a mathematical experiment

- **Finite procedure:** run a bounded search / sweep with recorded parameters.
- **Observable(s):** counts, gaps, residues, runtime scaling, or first counterexample witnesses.
- **Parameter space:** vary bounds (and sometimes algorithmic choices).
- **Outcome:** plots/tables + “witness objects” for failures.
- **Reproducibility:** outputs saved to `out/e015/` with a parameter snapshot.

## Experiment design

- **Computation:** bounded enumeration / sampling with explicit limits.
- **Outputs:** figures and a short `report.md` summarizing what was found.
- **Artifacts written:**
- `figures/fig_*.png`
- `params.json`
- `report.md`

## How to run

```bash
make run EXP=e015
```

or:

```bash
uv run python -m mathxlab.experiments.e015
```

## Notes / pitfalls

- “No counterexample found” only means “none found within the configured bounds”.
- For probabilistic tests (when used), treat outcomes as *evidence*, not proof.

## Extensions

- Increase bounds and rerun (recording runtime and memory).
- Compare alternative heuristics or algorithms on the same parameter grid.
- Turn found deviations into new, tighter conjectures.

## Published run snapshot

If this experiment is included in the docs gallery, include the published snapshot (report + params).

```{include} ../reports/e015.md
:start-after: "<!-- REPORT:BEGIN -->"
:end-before: "<!-- REPORT:END -->"
```

::: {dropdown} params.json (snapshot)
:open:

```{literalinclude} ../params/e015.json
:language: json
```

:::

## References

See {doc}`../references`.

## Related experiments

- {doc}`e047` (Fermat numbers: Pépin test + factor witnesses)
- {doc}`e002` (Even Perfect Numbers — Generator and Growth)
- {doc}`e003` (Abundancy Index Landscape)
- {doc}`e007` (Mersenne growth (bits and digits))
- {doc}`e008` (Lucas–Lehmer scan (prime exponents))