In the YouTube video The Reciprocals of Primes, Matt Parker explores the work of William Shanks, who was an English mathematician around 1870-1880. In the video, Matt shows ShanksBot, his Python program.

This is a Go implementation of ShanksBot.

The repository contains two binary files:

$ go run ./cmd/shanksbot

This is an interactive program that asks you to enter a positive prime number.

It calculates the number of periods of the reciprocal of the given prime number.

(Note that it also works with non-prime numbers.)

$ go run ./cmd/generator

William Shanks published a table of primes (and the periods of their reciprocals) up to 110,000.

This program prints this table to the screen. In the first column we have a prime number, and next to it you can see the number of periods of the reciprocal of the given prime number.

In the folder cmd/generator/, you can also find this table in a text file.

• The Reciprocals of Primes, on YouTube
• William Shanks, an English mathematician
• ShanksBot-RS, a Rust implementation of ShanksBot (related work)