Investigating Prime Sequences

This repository contains a Rust implementation of various primality tests, which powers a command-line utility for computing and visualizing prime sequences.

The distribution of primes and related numbers is not random, and certain properties of the corresponding sequences can be visualized using graphs such as the Ulam Spiral. Here is an example marking the prime numbers from 1 to 1000000 in a spiral arrangement on a square lattice:

Recurring patterns emerge in the visualization, notably lines and intersections. This software package provides ways to perform experimental mathematics on this topic, i.e. to study arbitrary sequences to identify properties and patterns.

Setup

Install Rust:

• curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh
• or update it with rustup update

Build the software package:

• cargo build
• cargo test
• cargo run [arg1] [arg2]

Clean the directory:

• cargo clean

Primality tests

The following types are available

• Primes: primes
• Pythagorean primes: pythagorean
• Semiprimes: semiprimes
• Squarefree semiprimes: squarefree-semiprimes
• Pernicious numbers: pernicious
• Prime powers: prime-powers
• Fermi-Dirac primes: fermi-dirac

Usage

On the command-line, unless the default is used all arguments have to be defined, argument order matters:

1. Number type (primes), see alternatives above
2. Start (1)
3. End (1000000)
4. Output type (b-file), alternative: graph

Examples:

• cargo run semiprimes 1 10 (outputs the first 10 semiprimes in the terminal)
• cargo run primes 1 100000 graph (generates two graphs, a sequential one and an Ulam spiral)