by Alex Durlak and Brian Richer

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M74207281 is the largest known prime number. Represented in scientific notation, the number is 274207281-1. Written out in words the number is “two to the power of seventy-four million, two hundred seven thousand, two hundred eighty-one, minus one.” Found in January of 2016 by the Great Internet Mersenne Prime Search, it is 22.3 million digits long.

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 behavior of an elaborate function called the Riemann Zeta function. The 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 three volumes of 274207281-1 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 meaning and a timeless, universal character 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  274207281-1 reveal the universe’s mathematical structure. Everything in the universe–including humans–are 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  274207281-1 books is to present the number in such a way that it may reveal some insight into the nature of Prime Numbers.

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. 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 poster is 36” wide and 50’ long. The number is set in 2.6 point type in Figgins Sans and printed giclée in black on an acid free, 100% cotton rag 340 gsm stock. It comes with a bent metal shelf to hold the poster made of 16 gauge rolled steel and is finished with a white, matte sandtex powder coat. It is printed in a limited edition of eleven.

Above: Jennifer Sciarrino