# E112: Prime race: π(x;q,a) − π(x;q,b)

```{figure} ../_static/experiments/e112_hero.png
:alt: E112 hero
:class: experiment-hero

E112: Prime race: π(x;q,a) − π(x;q,b)
```

**Tags:** `number-theory`, `prime-races`, `visualization`, `aps`, `primes`

## Highlights

- Focused numeric experiment with a small set of figures.
- Parameters saved to `params.json` for reproducibility.
- Defaults are chosen, so the experiment remains feasible for the CI “slow” suite.

## What is computed

- Compute prime counts in residue classes and plot difference curves for representative pairs.

## Notes

- This page summarizes the intent; see the generated `report.md` in `out/` for concrete outputs.

## Published run snapshot

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

```{include} ../reports/e112.md
:start-after: "<!-- REPORT:BEGIN -->"
:end-before: "<!-- REPORT:END -->"
```

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

```{literalinclude} ../params/e112.json
:language: json
```

:::

## References

- See `docs/background/primes-in-arithmetic-progressions.md` and `docs/background/prime-number-races.md`.

## Related experiments

- {doc}`e113` (E113: First prime in each residue class)
- {doc}`e072` (Prime race mod 4: pi(x;4,3) vs. pi(x;4,1).)
- {doc}`e073` (Prime race mod 3: pi(x;3,2) vs. pi(x;3,1).)
- {doc}`e074` (Prime race mod 8: leaderboard among 1,3,5,7.)
- {doc}`e075` (Prime race statistic: distribution on a log-grid.)