Two to the power of Seventy Four Million Two Hundred and Seven Thousand Two Hundred Eighty One minus One

M74207281 is the largest known prime number. Represented in scientific notation, the number is 2^74207281-1. Written out, the number is “two to the power of seventy-four million, two hundred seven thousand, two hundred eighty-one, minus one.” Found in January 2016 by the Great Internet Mersenne Prime Search, it is 22.3 million digits long.

The Two to the power of Seventy Four Million Two Hundred and Seven Thousand Two Hundred Eighty One minus One books are part of Castor Design’s continued exploration of scientific and mathematical principles; presenting universal truths in a simple, elegant way. Past projects with Castor’s Science and Humanities division have included an electron accelerator, a particle cloud chamber, and lighting projects using the wireless transfer of electricity. Brian Richer of Castor Design conceived of the books, which were designed with Alex Durlak of Perish Publishing. The books are part of a series that also includes a 50’ long poster at 2 pt font, t-shirts with the book’s title, and an Instagram feed @M74207281Prime posting 4900 digits of the number each day, complete in 2030.

A prime number is a natural number that has no positive divisor other than 1 and its itself, e.g. 2, 3, 5, 7, etc. They play an important role in pure mathematics and its applications. Though we have spent centuries working with prime numbers, their true nature and distribution remain a mystery. Based on Euclid’s postulate using the sequence of known prime numbers as building blocks for the larger primes that follow, we know that there are an infinite number of primes. However, they strangely occur less frequently as they get larger. German mathematician Bernhard Riemann observed that the frequency of prime numbers is very closely related to the behaviour of an elaborate function called the Riemann Zeta function: The Riemann hypothesis asserts that all solutions of the equation lie on a certain vertical straight line. A proof that would explain the distribution of prime numbers is one of the last great unsolved mathematics puzzles.

Each of the volumes of 2^74207281-1 is over 1300 pages long for a combined total of 3982 pages of the number’s digits. Despite the apparent randomness of prime numbers, the digits have significance whether we recognize the numbers as prime or not. G.H. Hardy wrote, “317 is a prime number not because we think so, or because our minds are shaped in one way or another but because it is so, because mathematical reality is built that way.”

Like the books in Borges’ Library of Babel whose seemingly random letters and punctuation served as building blocks for the basis of language and the universe, the digits within 2^74207281-1 reveal the universe’s mathematical structure. Everything in the universe, including humanity, is part of this structure. All matter is made of particles which have properties of charge and spin; these properties are essentially mathematical. Notwithstanding their apparent simplicity and fundamental character, prime numbers remain one of the most mysterious objects studied by mathematicians. The impossible task of the series is to present the number in such a way that it may reveal some insight into the nature of prime numbers.

Book Details
274207281-1 is published by Perish Publishing, Toronto in 2017. It is printed in a limited edition of ten, two artist’s copies and one display copy. This book is designed by Alex Durlak of Perish Publishing and Brian Richer of Castor Design. It was edited and set into type at Standard Form, then printed by Copywell and bound by Anstey Bindery in Toronto. Each edition is held by a honed Carrara marble bookend with a black reflective face.

The book is 7” by 10.5”, a ratio that follows the classic harmonic 2 : 3 proportions. The margin proportions follow the common medieval structure of 2 : 3 : 4 : 6. The cases are wrapped in white book cloth and the binding features black edge colouring, black
headbands and black endpapers. The covers and spine are printed on a letterpress in black and the colophon is printed on a letterpress in metallic silver on the endpapers. The inside pages were printed on a web inkjet press in black on Bible paper.

The titling face is Bauer Bodoni by Heinrich Jost for the Bauer Foundry in 1926 and is based upon a serif cut by Giambattista Bodoni in 1798. The body face is Figgins Sans by Nick Shinn for Shinntype and is based upon a series of sans serifs cut by the V. & J. Figgins foundry in 1836. The paper is Ethos Uncoated Inkjet, made at the Appleton Coated mill in Combined Locks, Wisconsin.