# E103: Chebyshev ψ(x): prime powers drive jumps

```{figure} ../_static/experiments/e103_hero.png
:alt: E103 hero
:class: experiment-hero

E103: Chebyshev ψ(x): prime powers drive jumps
```

**Tags:** `number-theory`, `quantitative-exploration`, `visualization`, `mangoldt`, `explicit-formula`

## 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

- Plot ψ(x) and highlight jump contributions coming from prime powers.

## 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/e103.md
:start-after: "<!-- REPORT:BEGIN -->"
:end-before: "<!-- REPORT:END -->"
```

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

```{literalinclude} ../params/e103.json
:language: json
```

:::

## References

- See the relevant references in `refs.bib`.

## Related experiments

- {doc}`e061` (Chebyshev ψ(x) and prime powers)
- {doc}`e104` (E104: von Mangoldt Λ(n): support and statistics)
- {doc}`e076` (Chebyshev θ(x;q,a): weighted prime counts in progressions.)
- {doc}`e080` (Chebyshev bias: leader fraction vs. x.)
- {doc}`e118` (E118: Chebyshev bias: lead-time statistics)