This is far from a comprehensive list of prime numbers -- if we were to compile and write out an exhaustive list of all known prime numbers, this would be a truly insufferable article to scroll through. Theoretically, there are infinite prime numbers in the same way that there are infinite numbers in general, but they become fewer and farther as you count higher and higher.
That certainly hasn't stopped mathematicians -- both professional and amateur -- from trying to ferret out new ones. In fact, in 1996, computer scientist George Woltman started a project known as the Great Internet Mersenne Prime Search (GIMPS) in order to do exactly that. And the search just got its first hit in almost 6 years.
Amateur number detective Luke Durant (a researcher and former employee of the software company NVIDIA) recently found the biggest prime ever discovered: 2-1, now also known as M136279841. According to a press release, the find was made on October 11 and confirmed on October 12, and the number is over 40 million digits long -- more than 16 million digits larger than the next largest prime.
M136279841, like all primes hunted down by GIMPS, is what is known as a Mersenne Prime. Named for French monk Marin Mersenne, who made a conjecture regarding how to find these numbers, Mersenne Primes are prime numbers that can be described by the expression 2-1. Basically, if you multiply 2 by itself p number of times and subtract 1 from that result, you get your prime. But not all values for p will produce a prime number, so the overall goal of GIMPS is to find values that work for p. This new prime is only the 52 Mersenne Prime ever discovered.
There are a few ways that prime hunters look for primes, but one of the most common is to have a computer perform hundreds of what are called Fermat primality tests. A possible prime number is run through a probabilistic scenario, and if it checks out, it's most likely a prime number. It's a solid strategy, but it has one major drawback -- it takes a lot of computing power.
And that's where Durant comes in. An amateur only in the most literal, doesn't-do-this-as-a-job sense, Durant is known as the most prolific contributor to GIMPS on account of his home-built, cloud-computing-based, GPU-boosted supercomputer (which he estimates, according to an interview with the YouTube channel Numberphile, cost "under $2 million"). Frustrated by the slow-going nature of his search on a basic computer, he acquired computing power from multiple companies -- even setting up an LLC for the project to get greater access to that computing power -- and juiced his calculations. According to GIMPS founder George Woltman, the project was receiving an average of 300 results a day from all participants together. Once Durant joined the search, that number jumped to an average of 3500.
Eventually, one of those searches hit, and the first prime to come out of GIMPS in over half a decade was revealed. For the most part, people hunt down these primes because it's interesting. They're the building blocks of all other numbers, after all (plus, if you hit one, there's a payout of $3,000). But primes also have an extremely important place in modern-day encryption. The more of them we can find, the more secure we can be.
But, also, the more we just... know. Some would say that knowing in and of itself is enough to justify the search. Whatever the motive, however, the hunt goes on.