E113: First prime in each residue class

E113: First prime in each residue class

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

• For each reduced residue a (mod q), find the smallest prime p≡a (mod q) and visualize results.

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_first_prime_per_residue.png

• params.json

• report.md

Notes

• RR(q) size: 8

• Missing residues within search bound: []

• This is a small-N version of the Linnik / least prime in AP story.

params.json (snapshot)

{
  "p_max": 200000,
  "q": 30
}

References

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

Related experiments

• E112: Prime race: π(x;q,a) − π(x;q,b) (E112: Prime race: π(x;q,a) − π(x;q,b))

• E023: Residue class distribution mod q (Residue class distribution mod q)

• E070: Primes in residue classes: pi(x; q, a). (Primes in residue classes: pi(x; q, a).)

• E081: Prime race sign changes: first crossings table. (Prime race sign changes: first crossings table.)

• E072: Prime race mod 4: pi(x;4,3) vs. pi(x;4,1). (Prime race mod 4: pi(x;4,3) vs. pi(x;4,1).)