# E104: von Mangoldt Λ(n): support and statistics

```{figure} ../_static/experiments/e104_hero.png
:alt: E104 hero
:class: experiment-hero

E104: von Mangoldt Λ(n): support and statistics
```

**Tags:** `number-theory`, `quantitative-exploration`, `visualization`, `mangoldt`, `arithmetic-functions`

## 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

- Visualize where Λ(n) is nonzero (prime powers) and summarize basic statistics.

## 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/e104.md
:start-after: "<!-- REPORT:BEGIN -->"
:end-before: "<!-- REPORT:END -->"
```

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

```{literalinclude} ../params/e104.json
:language: json
```

:::

## References

- See the arithmetic-functions background pages in `docs/background/`.

## Related experiments

- {doc}`e061` (Chebyshev ψ(x) and prime powers)
- {doc}`e103` (E103: Chebyshev ψ(x): prime powers drive jumps)
- {doc}`e118` (E118: Chebyshev bias: lead-time statistics)
- {doc}`e088` (E088: Zero counting via Riemann–von Mangoldt)
- {doc}`e093` (E093: −ζ′(s)/ζ(s) via the von Mangoldt series)