mathxlab.experiments.spiral_suite

Prime-visualization spiral suite (E124–E126).

Quickstart

from mathxlab.experiments.spiral_suite import run_e124, run_e125, ParamsE124

Public API

Name	Kind	Summary
ParamsE124	class	Parameters for E124 (Klauber triangle).
ParamsE125	class	Parameters for E125 (Sacks spiral).
ParamsE126	class	Parameters for E126 (hexagonal number spiral).
run_e124	function	E124: Klauber triangle: primes in a square-to-square triangle.
run_e125	function	E125: Sacks spiral: primes on r=sqrt(n), θ=2π sqrt(n).
run_e126	function	E126: Hexagonal number spiral: primes on a hex grid spiral.

Reference

Classes

class mathxlab.experiments.spiral_suite.ParamsE124(rows=301)

Bases: object

Parameters for E124 (Klauber triangle).

rows

Number of rows in the triangle. Row m contains integers from (m-1)^2 + 1 to m^2 (inclusive), so total integers are rows^2.

class mathxlab.experiments.spiral_suite.ParamsE125(n_max=250000)

Bases: object

Parameters for E125 (Sacks spiral).

n_max

Largest integer to place on the spiral (inclusive). Integers 1..n_max are mapped to polar coordinates r=sqrt(n), theta=2π sqrt(n).

class mathxlab.experiments.spiral_suite.ParamsE126(rings=150)

Bases: object

Parameters for E126 (hexagonal number spiral).

rings

Number of hexagonal rings around the center. The spiral contains 1 + 3*rings*(rings+1) integers.

Functions

mathxlab.experiments.spiral_suite.run_e124(*, out_dir, seed, figures_dir, report_path, params_path, rows=301)

E124: Klauber triangle: primes in a square-to-square triangle.

In the Klauber triangle, row m contains the integers:

(m-1)^2 + 1, (m-1)^2 + 2, …, m^2

i.e. between consecutive squares. Highlighting primes reveals striking vertical streaks for certain quadratic prime-rich sequences.

Parameters:

• out_dir – Experiment output directory.

• seed – Deterministic seed for reproducibility (not used here).

• figures_dir – Directory for figure artifacts.

• report_path – Path to the Markdown report.

• params_path – Path to params.json.

• rows – Number of rows (must be positive).

mathxlab.experiments.spiral_suite.run_e125(*, out_dir, seed, figures_dir, report_path, params_path, n_max=250000)

E125: Sacks spiral: primes on r=sqrt(n), θ=2π sqrt(n).

Parameters:

• out_dir – Experiment output directory.

• seed – Deterministic seed for reproducibility (not used here).

• figures_dir – Directory for figure artifacts.

• report_path – Path to the Markdown report.

• params_path – Path to params.json.

• n_max – Largest integer to plot (inclusive).

mathxlab.experiments.spiral_suite.run_e126(*, out_dir, seed, figures_dir, report_path, params_path, rings=150)

E126: Hexagonal number spiral: primes on a hex grid spiral.

Parameters:

• out_dir – Experiment output directory.

• seed – Deterministic seed for reproducibility (not used here).

• figures_dir – Directory for figure artifacts.

• report_path – Path to the Markdown report.

• params_path – Path to params.json.

• rings – Number of rings around the origin (>=0).