Supercomputing and prime numbers in Mathematics Today!
Posted: 6 Jan 2014 | 14:51
As a follow-up to speaking at the British Science Festival in Sept 2013, I was asked to write an article for the Institute of Mathematics & its Applications about the PrimeGrid project. The full article is available online, or in the Dec 2013 edition of the Mathematics Today magazine.
Prime numbers are among the most basic yet mysterious objects in mathematics. There are infinitely many primes, and there are heuristics for their distribution, but no efficient method exists for generating a list of prime numbers a priori without simply testing each candidate integer in turn. For any given (large) number, determining its factors - the prime numbers which can be multiplied together to produce it - is even harder. This gives rise to a number of strong encryption and security algorithms such as RSA which work because it is computationally infeasible to determine the private key used to encrypt a message.
The search for large prime numbers is also linked closely to the development of supercomputers. From the 1950s, when the first 600-digit primes were found using the EDSAC-2 and SWAC computers based on valve technology, up until the dominance of the Cray 1, Cray X-MP and Cray-2 in the 80s and early 90s, only such exclusive machines were fast enough to complete the demanding calculations needed to prove primality of large numbers. The personal computer boom in the mid-1990s with the release of the Intel Pentium and cheap desktop hardware changed all that, and since then prime searches have been carried out using 'grids' of loosely coupled commodity computers run by volunteers. Of course, things eventually come full circle, and today the majority of supercomputers now use commodity Intel or AMD processor technology!
If you're interesting in finding out more about PrimeGrid, or how to contribute your computing time to the project, visit www.primegrid.com
The image above shows a Cray T94 supercomputer, similar to the one used to prove primality of 21257787–1 in 1996. Photo from www.craysupercomputers.com.