Prime Numbers Museum

This page was created on June 9, 2021

This page was last updated on October 18, 2025.

Featured Collection

77-digit prime number without the digit "7" (I have a 777-digit one too)

7013-digit prime number (2021)

Proth Prime (of the form k×2ⁿ+1)

Rubik's Cube Prime (2020)

4096 digits, arranged in a 64×64 square.

Only five different digits: 1, 4, 5, 7, 8

I've always been fascinated by prime numbers, so much so that it alone was enough to motivate me to study math in university.

Prime numbers are incredibly rare, especially very large ones.

Here are a collection of interesting, large, or artistic primes that I've found.

What are prime numbers?

Prime Numbers are numbers that can only evenly divide into themselves and 1. For example, the number 7 is prime because the only way it can be split up is into groups of 1, or groups of 7 (itself). 6, on the other hand, is not a prime number, because although you can also split 6 into groups of 1, or groups of 6 (itself), it can also be split into two groups of 3 or three groups of 2. A number is only prime if it only divides evenly into 1 and itself.

For anyone interested, here are the prime numbers up to 100:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

WRDSB Prime Number.pdf

WRDSB Prime

October 7, 2020 / Digits: 1967.

This was the first ever "big prime number" that I found, and is the number that started this entire journey.

As a Grade 8 student of Centennial Public School in 2020, two classmates (Jerry Wang, Russell Morland) and I were inspired by the Trinity Hall Prime, a number featured on Numberphile in 2017.

We wanted to do something similar, except applied to our middle school. We eventually decided that the Centennial Public School logos at the time were all extremely hard to showcase well, so we made one with the logo of the school board (Waterloo Region District School Board).

We wanted the prime to be 1967 digits long, because Centennial was opened in 1967 to celebrate the 100th anniversary of Canadian Confederation. However, 1967=7×281, which are infeasible dimensions for a rectangular image. Instead, we used the fact that 48×41=1968, and created a 48×41 image, except the last (48th) row only has 40 digits.

This, alongside the Rubik's Cube and Science Walrus, were found with Russell and Jerry. The rest of them were found independently.

You can read more about this number in the little write-up I created all those years ago in 2020, as a 13-year-old. I sure hope my writing skill has gotten better since then.

Rubik's Cube

Rubik's Cube Prime.pdf

Science Walrus

Science Walrus Prime Number.pdf

Prime Numbers have always fascinated me. Nothing was more out of this world to me than a big number that is resistant enough to not divide into anything smaller than it, a number that can't be broken up into equal groups. I wish to learn more about the mathematics involved in prime numbers, as properties of prime numbers are still quite a poorly understood topic in number theory and mathematics.

Primes can be categorized in many different ways. The reason why primes are categorized, is because testing a random odd number for it's primality is much less likely to turn up prime, than some expression that generates a specific list of primes.

For example, a Mersenne Prime (named after Marin Mersenne, a French Mathematician and Physicist) is a prime of the form 2ⁿ - 1 (essentially you multiply a bunch of 2's, then subtract 1). I am not actually going to invest time into finding these, as all of the ones that are 1000 to 10000 digits long have been found long ago, and software already exists to find the largest ones. Nine of the top ten largest primes are Mersenne Primes, the largest (as of October 2025), being 2¹³⁶²⁷⁹⁸⁴¹-1, at over 41 million digits long.

I'm more invested in finding Proth Primes, which are very similar. You multiply any number, let's say 19, by once again, a power of 2, then add 1. In this case, it would be 19×2ⁿ+1. People aren't invested into primes of this form, so I guess I'm claiming the spot before other people do I guess?

I also occasionally find near-repdigit primes. The term 'rep-digit' is shorthand for 'repeated digit', which is defined as exactly what it sounds like: a repeated digit! Examples of 'rep-digits' are 11, 555555, 666666666666666, and 99999999999999999. With the exception of repeated 1's (e.g. 11, 1111111111111111111), rep-digits are never prime. For example, 8888888 is not prime, because it is clearly divisible by 8 (and 1111111 for that matter). However, you can't guarantee that a number isn't prime if you just change one of the digits, such as the number 333331, a prime number. near-repdigit prime numbers are primes that have all the same digits, with just one digit that is different from the rest.

Finally, I'll mention Picture Primes, which are primes that when arranged in a certain grid format, looks like a picture of some sort.

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