E117: Prime-counting approximations: li(x) and friends

E117 hero

E117: Prime-counting approximations: li(x) and friends

Tags: number-theory, model-checking, visualization, li-x, pnt, bounds

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

  • Compare π(x) to li(x) and related approximations and visualize the signed error.

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_functional_equation_residual.png

  • params.json

  • report.md

Notes

  • max relative residual on grid: 3.03e-16

  • This checks numerical consistency of chi_factor and mpmath zeta implementation on a small grid.

params.json (snapshot)
{
  "dps": 70,
  "sigma": 0.2,
  "t_max": 25.0,
  "t_steps": 60
}

References

  • See the relevant references in refs.bib.