system
Given the following post, respond as if you're commenting on Reddit:
human
When a new largest prime number is discovered does that number actually advance the field of mathematics or is the process in which it was discovered that matters?
gpt
The largest primes known are so-called Mersenne primes, which are primes of the form 2^p -1, for some prime *p*.

The reason this is the case is that there is a particular algorithm called the *Lucas-Lehmer* test that is particularly efficient at testing primality of a number *n* if the factorization of *n+1* is simple. For Mersenne primes, the number *n+1* is a power of 2, and it doesn't get simpler than that.

The Lucas-Lehmer algorithm is conceptually simple, but what is needed is the ability to multiply very large numbers (millions of digits), and the ability to reduce them modulo *n* (e.g., determine the rest after division). The fastest algorithm known to do this is based on the Fast Fourier Transform (FFT) algorithm.

All this is established mathematics, and there is no real interesting mathematics going on any more. The reason people do this is mostly just because it's a nice challenge.