Three Dog Night got it wrong. One is not the loneliest number. Not by a very long shot. At the moment, the loneliest number we know of is 2^74,207,281-1 .

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Floating far, far out there on the numberline, it is an absolute, uncomplex immensity all by itself, a mountain among molehills. The World’s Largest Known Prime Number is the ultimate symbol of unrestrained rationalism, a perfectly clear and distinct concept of crystaline, logical mathematics. Yet , both through its own process of discovery and its aggressive stretching of our linguistic frontiers, it also reveals the absurd side of this same paradigm. It challenges straightforward epistemological claims for the primacy of mathatics, for here is an example of something we might claim to know but find very difficult, perhaps even impossible to SAY (rather like the way certain mystical traditions treat the name of God). Even our claims to knowledge here seem quite thin, in spite of the quite straightforward propositional nature of the sentence “2^74,207,281 -1 is prime”. What is its content of this sentence if the number itself in some sense cannot be known? And yet, unlike the even bigger number that comes right after it, about which we only know that it is “even”, about THIS number we know something quite special and difficult to discover: it is “prime”.

As a reminder, a prime number is a number that only has “1” and itself as divisors. It cannot be divided by any number without leaving a remainder. So, for example, the only way to get “17” is by multiplying 1 and 17. They are, so to speak, mathematically isolated, alone and invulnerable. They are in a sense the building blocks of the numerical universe.

Most of us can figure out the first few primes (2, 3, 5, 7, 11, 13, 17 and so on). However, there is no clean straightforward formula that can be used to discover whether a given number is prime. Take a number like 117, which might “look” rather prime. If you want to discover whether or not it is prime, you have to actually go about trying to divide it by all its possible divisors and see if there are any (there are – 9 x 13). This makes prime numbers rather difficult to figure out, and also makes them extremely useful for cryptography. Apparently, most of our credit card and online banking security is ultimately dependent on prime numbers.

Dr. Curtis Cooper

Hence discovering prime numbers, particularly big ones, is a significant mathematical and computational challenge, and many mathematicians and computer scientists have devoted considerable energy to the effort.  For example, the Great Internet Mersenne Prime Search (GIMPS) is an organization devoted to trying to discover the world’s largest prime number through crowdsourcing, using a large network of ordinary people’s computers to help do the immense amounts of math involved.  In 2009 they were awarded US\$100,000 by the Electronic Frontier Foundation for their discovery that 2^43,112,609-1 is indeed prime! This is a very big number, almost 13 million digits long. However, since then two even larger primes have been discovered, the most recent by Dr. Curtis Cooper of the University of the University of Central Missouri (along with a team including G. Woltman, S. Kurowski, GIMPS, et al.) There is still an open reward of a MILLION dollars for anybody that discover a prime number of a billion digits.

Trying to get our heads around a number this size has proved difficult. It is possible to print the digits themselves using a small font – they create NYC telephone-directory sized volumes. They are can be viewed online, though even with a good internet connection they take a while to load. But this just generates an enormous scrollable page full of numbers which, while impressive, fails to fully communicate the gravity of this number. However, through the great work of Landon Curt Knoll (to whom we owe a debt of gratitude for helping to realize this project), it is possible to discover the English-language equivalent of any number. What does this mean? Well, most people are quite familiar with some biggish numbers, up to the millions, billions, and trillions. But such names are just the tiniest beginnings of our named numberline. After trillions there are quadrillions, quintillions, sextillions, septillions, octillions, nonillions and decillions. And things don’t stop there, they just keep getting bigger, as you can discover for yourself at Dr. Knoll’s site, or by just listening to our podcast.

Projective City is attempting to provide a new way to encounter this number by reading the entire thing out loud. Our initial idea was to seek the assistance of volunteers to help read out loud pages of the number. We began in 2011, with volunteers trickling in here and there to read the number 2^43112609-1 on camera. Unfortunately, we didn’t get the 20,000 or so volunteers we were hoping for. Instead, we got something like 35. Still, though shy of the mark, the project yielded some fruitful results. However, the whole project became moot in 2013, when Dr. Cooper’s team discovered an even bigger prime. So now that project has been archived (click here to review the collection of videos), and in response, we began a podcast of the number.

Our brave volunteers who sent us videos of themselves reading pages

But yet again, Dr. Cooper’s impressive computational abilities were too fast for us, and a new, even larger number was discovered at the beginning of January 2016. This has prompted the third attempt, which will also take the form of a Podcast, which will continue at least until another, larger number has been discovered.

Bear in mind that we are not here talking about infinity. The idea that we cannot get our heads around the infinite is something of a cliche, a truism of our human condition at least since the time of Kant. And, as a cliche, it is quite easily dismissed or somehow ignored as the mere pathos of romantics. Well, this number has no claims to any sort of airy-fairy infinity shmaltz. This is a real-deal, honest-to-goodness NUMBER. It is a number composed of millions of digits, but definitely still well short of infinity. So it isn’t just the infinite we cannot face. We can’t even get as far as halfway.

We hope you will enjoy listening to these podcasts as we all seek to come to grips with the huge and incomprehensible things that seem to comprise an ever greater amount of the world in which we live.