Prime Number Art: How Mathematicians Create Images with Huge Prime Numbers

A classic way to make art with a computer is using ASCII characters, but the practice even predates the creation of code and personal systems. What happens when we use more precise rules—say, prime numbers? Some mathematicians have not only managed to reproduce things like maps and coats of arms, but they've also gone as far as controlling the number of digits used.

A Mathematical Coat of Arms

The story begins with a video published by the Numberphile team in September 2017. They explain that mathematician James McKee left a farewell gift at Trinity Hall, Cambridge: an unusual representation of its coat of arms. The general shape is easy to identify, but if you look closer, you'll find that it's made of a giant number that is also prime:

The number has 1,350 digits, and it is not accidental: it's the year Trinity College was founded. So McKee reproduced the institution's coat of arms using a prime number with exactly 1,350 digits. It's a (more or less) simple challenge for a well-prepared mathematician, but he's not alone. Other enthusiasts have decided to repeat the process, with even more surprising results. For example, here's a famous portrait of French writer Georges Perec with his cat, transformed into a prime of 3,225 digits:

Prime Number Art: Images in Giant Numbers — The shape of the cat is very well done...

A Map, a Masterpiece, and More

Then there's the work of physicist Gilles Esposito-Farese, who also drew inspiration from McKee to find a prime of 2,258 digits that, when converted to binary, gives us nothing less than a Mercator projection. Even more impressive is this reproduction of da Vinci's Mona Lisa, which uses a prime of 30,000 digits. I personally recommend viewing its PDF version.

Prime Numbers as Text

The next two examples show that generating text with prime numbers is perfectly possible. One is in English and the other in French, with 5,000 and 6,000 digits respectively. In both, the dominance of the number 7 is remarkable:

A Final Example

Finally, there's the work of another Trinity member, a student named Jack Hodkinson. The day after the video about McKee's prime number was published, Hodkinson created his own version of Corpus Christi College, which also hides his initials and birth date. The total digits amount to 2,688.