E112: Prime race: π(x;q,a) − π(x;q,b)

E112 hero

E112: Prime race: π(x;q,a) − π(x;q,b)

Tags: number-theory, prime-races, visualization, aps, primes

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

  • Compute prime counts in residue classes and plot difference curves for representative pairs.

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_prime_race_diff.png

  • params.json

  • report.md

Notes

  • Final lead at p_max: -64

  • The diff changes sign; persistent bias is subtle and depends on q,a,b.

params.json (snapshot)
{
  "a": 1,
  "b": 3,
  "p_max": 800000,
  "q": 8
}

References

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