Exhibiting Randomness in Arithmetic using Mathematica and C

TL;DR

This paper presents a comprehensive software package in Mathematica and C that demonstrates the presence of randomness in arithmetic through a complex, large-scale equation, illustrating concepts from algorithmic information theory.

Contribution

It provides the complete Mathematica code and C implementation for constructing a large equation proving randomness in arithmetic, previously only described in a book.

Findings

The software successfully constructs a million-character equation.

Mathematica code is compact but slow, C code enhances performance.

The work illustrates the application of algorithmic information theory in arithmetic.

Abstract

In my book "Algorithmic Information Theory" I explain how I constructed a million-character equation that proves that there is randomness in arithmetic. My book only includes a few pages from the monster equation, and omits the software used to construct it. This software has now been rewritten in Mathematica. The Mathematica software for my book, and its input, are here in their entirety. The Mathematica code is remarkably compact, but it sometimes is slow. So one C program plus equipment for automatically generating another is also included in this software package.