Distributed internet prime number search PrimeGrid has found a new largest generalised Fermat prime.
The discovery was made on 29th August, and was double-checked before being announced on 2nd September. PrimeGrid uses a distributed computing approach and uses spare computer time donated by volunteer computers connected to their network.
A generalised Fermat prime is a prime number of the form $a^{2^n} + 1$, with $a \gt 0$. It’s called ‘generalised’ because ‘Fermat prime’ is the name for the particular case $a=2$.
Much like Mersenne primes, there are special tests which make it much easier to check if a number of this form is prime than for a general number. For this reason, they’re a good place to look for new large primes.
Until now only 392 generalised Fermat primes had been found: this new discovery makes 393. At 6,253,210 digits long, it’s now the 12th largest of all known primes, and the second-largest known non-Mersenne prime.
PrimeGrid have put out an announcement in PDF format giving some more details about the search, and credits for the many people involved writing algorithms and providing computers to run them on.
The PrimeGrid homepage has more information about the many different prime number searches they run, and how to join in the search with your own PC.
The British Science Festival is organised annually by the British Science Association, and this year it’s hosted by the University of Brighton and the University of Sussex from Tuesday 5 to Saturday 9 September. For more details and full listings, see 
The next issue of the Carnival of Mathematics, rounding up blog posts from the month of July, and compiled by Kartik, is now online
Every August a multitude of comedy shows, theatre pieces, interpretive dance performances, musical extravaganzas and spoken word events spring up all over the Edinburgh Fringe. As a busy mathematician (there are infinitely many integers; who has spare time?) I’m sure you’ll appreciate our guide to which of those things are mathematical, or have a tangential (LOL) relationship with mathematics. Please note: none of these are recommendations, as we haven’t seen the shows and mainly have been grepping the word ‘maths’ in online programmes.