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

E103 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).

Artifacts

  • figures/fig_01_psi_minus_x.png

  • params.json

  • report.md

Notes

  • Nonzero Λ(n) terms up to N (prime powers): 18120

  • ψ(x) is the summatory von Mangoldt function and jumps at prime powers.

params.json (snapshot)
{
  "n_max": 200000,
  "stride": 5
}

References

  • See the relevant references in refs.bib.