## How to Memorize the Largest-Known Prime Number

**Portside Date:**

**Author:**Evelyn Lamb

**Date of source:**

A few weeks ago, a computer owned by Patrick Laroche of Ocala, Florida discovered a mathematical treasure, a new largest known prime number. Known as M82589933, it has 24,862,048 decimal digits. If you’d like to read more about it, check out this article I wrote for Slate two years ago (and updated a year ago). Though I did not write that article about this particular largest known prime number, I did write it about a previous largest known prime numbers, and M82589933 is yet another verse of the same song.

Today, I want to help you experience this new prime number viscerally by memorizing it.

I don’t know about you, but there’s no way I’m memorizing a 24,862,048-digit number. Instead, I’m going to memorize an easier 82,589,933-digit number using the magic of binary. The newest prime is a Mersenne prime, meaning it is one less than a power of two. In binary, numbers are written using only the digits 0 and 1. One is 1, two is 10, three is 11, four is 100, five is 101, and so on. Any power of two is a 1 followed by some number of zeroes. We saw that two is 10 and four is 100. The pattern continues: eight is 1000, sixteen is 10000, and so on. In base ten, if you subtract 1 from a 1 followed by a bunch of zeroes, you get a bunch of nines. (E.g. 1,000-1=999.) In base two, 1000-1=111. Any number one less than a power of two is a string of 1’s.

The new prime number is 2^{82,589,933}-1. In binary, that is a string of 82,589,933 ones. Easy peasy. The difficult part of memorizing it is keeping track of how many ones there are. Buckle up because I have some ideas for that, too.

In the first place, we do need to memorize the number of binary digits this number has. That’s 82,589,933. Try this handy phrase: “Cabbages in April besmirch September asparagus. And how!” The number of letters in the word correspond to the digits of the number, and it’s easy to remember because April cabbages are indeed better than September asparagus (in the northern hemisphere).

Now that we’ve memorized the number of digits, it would be nice to find a way to keep track of where we are in the digits as we start writing or reciting ones. The word TWENTY NINE is made from 29 straight line segments. Thus, it is an elaborate way to write the number 29 in tally marks. I decided to expand on the idea. First, I looked for famous poems or phrases that use no round capital letters. The Declaration of Independence, the Gettysburg Address, “The Waste Land,” and “The Jabberwocky” all disappointed me immediately. It was clear: I had to create my own. The following is a poem I wrote to help you get through it all. When written in capital letters, the poem uses 500 straight line segments (punctuation is not included).

Amenity twenty nine:

Lie lazily,

a fizzy affinity

familial, alien

with hymnlike alkalinity.

We twelve examine finality.

The lake,

a wink,

an inky inlet.

Exit we the fiftieth line,

Tie a tiny thymey tine.

Waltzlike I talk.

Timelike we walk.

If you wish to write the new prime number, you can write this poem in block letters 165,179 times--each straight line segment is a number 1--and then add 433 more ones. Alternatively, if you wish to recite the number, you can write the poem down 165,179 times while saying the word "one" with every stroke and then say "one" 433 more times.

Some challenges still remain in memorizing M82589933. How do you keep track of how many times you have written the poem? Do you get to take bathroom breaks while you demonstrate that you have memorized the new prime number? What happens if a larger prime is discovered while you are still in the middle of writing this one down? I am confident you will find innovative ways to tackle these challenges and revel in the full splendor of M82589933.

*Evelyn Lamb is a freelance math and science writer based in Salt Lake City, Utah.*