E123: π(x;q,a) vs. a simple baseline

E123 hero

E123: π(x;q,a) vs. a simple baseline

Tags: number-theory, prime-races, model-checking, visualization, aps, 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;q,a) to a baseline x/(φ(q) log x) and visualize deviations.

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_correlation_matrix.png

  • params.json

  • report.md

Notes

  • Variables: [‘log n’, ‘mu’, ‘phi/n’, ‘tau’, ‘sigma/n’, ‘omega’, ‘Omega’]

  • Strongest |corr| pairs (name1, name2, |corr|): [(‘phi/n’, ‘sigma/n’, 0.8944), (‘tau’, ‘Omega’, 0.8619), (‘sigma/n’, ‘Omega’, 0.856), (‘tau’, ‘sigma/n’, 0.8556), (‘phi/n’, ‘omega’, 0.7562), (‘phi/n’, ‘Omega’, 0.7209), (‘sigma/n’, ‘omega’, 0.7199), (‘tau’, ‘omega’, 0.7186)]

  • Interpret cautiously: many variables are highly non-Gaussian and arithmetic in nature.

params.json (snapshot)
{
  "n_max": 80000,
  "stride": 1
}

References

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