Volunteers have claimed to have found the largest prime number yet — twice within a fortnight! The two new record breakers are both Mersenne primes: numbers which can be written in the form 2p-1, where p is also prime.
Every whole number can be written as a product of prime numbers in a unique way, and this is why the primes are regarded as the building blocks of number theory. Mathematicians have known since antiquity that there are infinitely many primes, but there isn't a formula which describes them all. To check if a number is prime, you have to go through painstaking algorithms that take up a huge
amount of computing power. The task becomes easier when the number you're checking for primeness is a Mersenne number of the form described above.
But still, one computer isn't enough to do the job: the eleven previous largest prime discoverers have all been part of the Great Internet Mersenne Prime Search (GIMPS), which uses the computing power "donated" by tens of thousands of volunteers to chomp through the necessary calculations. The previous record prime — found in September 2006 — would have
taken an ordinary PC 4000 years to find, but with the help of a 70,000 strong computer network, able to perform 22 trillion calculations per second, popped out in "only" nine months.
Why would anyone want to find the largest prime to date? For the fun of it, of course, in true nerdy-style, but there's the added bonus of a $50,000 prize for the first to discover a prime with 10 million digits. On a less frivolous level, primes are extremely useful in cryptography: because factorising large numbers into their prime factors is so
computationally expensive, these factors can, and do, serve as almost unbreakable keys to encrypted messages — like the ones we send over the Internet every time we use our credit cards or send encrypted emails.
Experts are now performing independent checks to verify that the two new numbers really are prime, and are due to report back soon.
To find out more about GIMPS, previous Mersenne prime discoveries, and the role of primes in cryptography, read the Plus articles
How long will you live? How should you write down numbers? Who's your ideal partner? How good is our voting system? And what is a differential equation? These are difficult and momentous questions. This issue of Plus has some answers, along with a tour of digital art and the usual range of podcasts, news and reviews.
In this issue...
Understanding uncertainty: How long will you live?
It's impossible to give a precise date, but using mortality figures from people similar to you, you can make a confident guess. This article tells you how and has an interactive life expectancy calculator. Do you dare to find out?
Kissing the frog: A mathematician's guide to mating
What's your strategy for love? Hold out for The Only One? Or try and avoid the really bad ones? How long should you wait before cutting your losses and settling down with the next best who comes along? John Billingham investigates and saves the national grid in the process.
Mathematics and democracy: Approving a president
Much criticism has been levelled at the US voting system, and with this being election year, we're bound to hear more of it. In this article Steven J. Brams proposes an alternative voting system that could help make things more democratic.
The fabulous positional system
According to one mathematician, god created the whole numbers, with everything else being the work of humanity. Why, then did god not equip us with a good way of writing them down? Chris Hollings reveals that our number system, much used but rarely praised, is in fact a work of genius and took millennia to evolve.
Peter Markowich is a mathematician who likes to take pictures. At first his two interests seemed completely separate to him, but then he realised that behind every picture there is a mathematical story to tell. Plus went to see him to find out more, and ended up with a pictorial introduction to partial differential equations.
Computer-generated art is on the rise, and with it comes a further blurring of the boundaries between maths and art. Lewis Dartnell looks at some stunning examples.
Career interview: Systems engineer
Chuck Gill caught the space bug as a child when watching Alan Shepherd launch into space. Since then he's worked as a US Air Force navigator, a satellite operator, and in the US intelligence service. These days he's busy reducing carbon emissions and preparing London for the 2012 Olympics. Plus went to see him to find out more about his career.
Teacher package: Group theory
This issue's teacher package brings together all Plus articles on group theory, exploring its applications and recent breakthroughs, and giving explicit definitions and examples of groups. It also has some handy links to related problems on our sister site NRICH.
The world's biggest physics experiment is due to kick off on September the 10th, when the European Organisation for Nuclear Research (CERN) switches on the Large Hadron Collider (LHC). Never being one to miss out on such exciting events, Plus has put together a short guide for beginners.
Facebook is the online social network of choice at the moment, so who are we to buck the trend?
If you are a member of Facebook, you can now "become a fan" of Plus. Visit the Plus page on Facebook by clicking on this link. Here we will update the Facebook world of Plus news, views and events. Looking forward to seeing you there!
Peter Markowich is a mathematician who likes to take pictures. At first his two interest seemed completely separate to him, but then he realised that behind every picture there is a mathematical story to tell. Plus went to see him to find out more, and ended up with an introduction to partial differential equations. This podcast accompanies the article Universal pictures.