2^{43112609}-1 is the world’s largest known prime number. Written down in full it’s 12,978,189 digits long. That would take a long time to read out, let alone scream. It would be much simpler to type it out. Maybe.

Reproduced in real life this number would stretch for up to 32km. Depending on the typeface. Different fonts apparently produce markedly different results.

Prime numbers are also, apparently, useful for things other than cryptography.

In case you’re wondering, prime numbers aren’t just the stuff of academic longhairs: like typefaces, they have interesting properties that make them strangely useful. The classical example comes from mechanical engineering, where two meshed gears will wear most evenly if each has a coprime number of teeth, since this evenly distributes the possible ways in which they interact (thereby minimizing the effects of any irregularities.) Some have suggested that 13- and 17-year cicadas each follow prime numbered life cycles in order to ensure that their populations compete as little as possible, coexisting only once every 221 years.

## Comments

Little typo above.

2^43112609 isn’t prime. I wish I knew that because of my impressive sevant-like mental calculating abilities. However, I know this because of going to an Adam Spencer lecture at the Piazza at SouthBank one Friday night during Uni (wow, I really lived it up at QUT)!

I assume, if your sources are correct that 2^43112609

-1is Prime. It’s called a Mersenne Prime, named after a medieval Priest who thought he had worked out a way to calculate prime numbers, but he hadn’t.Just in case some poor kid (or university professor) comes this way looking for some Prime information, 2^43112609 isn’t the largest prime number. It’s not even prime (though it is very large).

I assume that the number you’re looking for is 2^43112609-1, which is quite possibly prime (and might be so if 43112609 is prime) and is definitely almost as large a number as 2^43112609.

These numbers are called Mersenne primes, named after a clergyman from a long time ago who thought he had worked out a way to find prime numbers. He hadn’t.

You are of course correct – and an even number is never a likely candidate for a prime.

That was a copy and paste failure on my part. I was so keen to get the superscript copied correctly that in my haste I missed the -1.

sorry about the double post. For some reason when I came back to your blog later in the day the comment hadn’t come up, and so I wrote another, shorter, comment.

Now I just look like I’ve got comment stutter.