Prime spirals

Using Ulam, Sacks, or Archimedean spirals as visualizations of prime survivors.

Plain

The idea

Prime spirals make something surprising visible: primes do not look like uniform noise.

PT can use them as a pedagogical showcase: when the sieve acts, survivors keep alignments, bands, and geometric traces.

Standard

A spiral does not prove a law. It turns an arithmetic sequence into an image and reveals correlations the eye grasps quickly.

For the mathematics section, it is an excellent plain-language bridge: one sees before calculating why survivors have geometry.

Technical

The PT_SPIRALS project can provide figures comparing Ulam, Sacks, and Archimedean spirals, with checks by modular classes.

The status should remain visual and exploratory unless a precise modular statistic is computed and referenced.

GitHub repository to publish: Igrekess/PT_SPIRALS; monograph ch01_sieve.

$n\mapsto r(n)e^{i\theta(n)}$

$\text{modular class}\rightarrow\text{visual alignment}$

public code

The links below point to public resources or planned GitHub repositories. No local working path is exposed to the reader.

GitHub

Igrekess/PT_SPIRALS

GitHub repository to publish before this can become a download link.

Pyodide not loaded.

Produces coordinates for a few prime points on an Archimedean spiral.