We’ve had a bit of a break over the holidays, but mathematical news stops for no mince pie. From new prime numbers to mathematical doodling challenges, here’s a round-up of some of the facts/stories that we’ve seen while trying not to do any work.
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$2^{77,232,917}-1$ is the new $2^{74,207,281}-1$
We now know 50 Mersenne primes! The latest indivisible mammoth, $2^{77,232,917}-1$, was discovered by Great Internet Mersenne Prime Search user Jonathan Pace on the 26th of December 2017. As well as being the biggest Mersenne prime ever known, it’s also the biggest prime of any sort discovered to date.
GIMPS works by distributing the job of checking candidate numbers for primality to computers running the software around the world. It took over six days of computing to prove that this number is prime, which has since been verified on four other systems.
Pace, a 51-year old Electrical Engineer from Tennessee, has been running the GIMPS software to look for primes for over 14 years, and has been rewarded with a \$3,000 prize. When a prime with over 100 million digits is found, the discoverer will earn a \$50,000 prize. That probably won’t be for quite a while: this new prime has $23{,}249{,}425$ decimal digits, just under a million more than the previous biggest prime, discovered in 2016.
If you’re really interested, the entire decimal representation of the number can be found in a 10MB ZIP file hosted at mersenne.org. Spoiler: it begins with a 4.
More information: press release at mersenne.org, home of the Great Internet Mersenne Prime Search.
New Mersenne prime discovered, and promptly printed out
Breaking news! On 19th January 2016, the Great Internet Mersenne Prime Search discovered a new largest prime number – we know 49 Mersenne primes, the largest of which is now $2^{74207281}-1$, a number containing over 22 million digits and full of primey goodness.
Internet Maths Person Matt Parker has responded to the news in spectacular style, by issuing a 14-minute long video explaining the discovery and its implications, as well as somehow scoring an interview with the actual discoverer of the new prime, Curtis Cooper.
New Mersenne primes not discovered
The Great Internet Mersenne Prime Search, the premier distributed-computing prime finding initiative, has reported that $M_{32582657} = 2^{32,582,657}-1$, the 44th Mersenne prime to be discovered, is also the 44th Mersenne Prime in numerical order. It was found by Steven Boone and Curtis Cooper in 2006 (Cooper also discovered the current largest prime as reported here in February), but until now it was not known for certain that other, smaller primes had not been overlooked. GIMPS has now checked all the intervening Mersenne numbers for primality and having found nothing, $M_{32582657}$ is secure in its 44th-ness.
Further information
The Great Internet Mersenne Prime Search (announcement on the front page as of November 10)
Their page for the prime itself
Mersenne Prime at Wolfram Mathworld
via @mathupdate on Twitter
Art for a maths department
I don’t think the university maths department I work in has enough art in it. I have gazed covetously upon the walls of other departments I visit, covered with beautiful mathematically-inspired paintings and inspirational posters, serving as a backdrop to cabinets full of geometrical curiosities. I recently suggested to our Head of School that we could buy some art, and he said “That’s a good idea. Send me some suggestions.”
I was pretty delighted with that response, so I spent an enjoyable hour trawling the internet for art that would inspire and enrich our students and staff. We don’t really have anywhere obvious to put sculptures, so I wanted something you can hang on a wall. I had no idea how much money the Head of School was thinking of spending, so I assumed the worst and tried to stick to cheap posters and prints as a starting point. I wasn’t just looking for art – anything to decorate the walls, even if it ends up teaching the students something, is desirable.
My first port of call was my Arty Maths blog. I’ve been collecting nice bits of art that invoke or involve maths (and not art created purely to represent maths) for almost two years now. Unfortunately, it turns out I’ve almost exclusively been collecting sculptures and video works. That meant I had to do some googling!
Because I found some nice things, and in case anyone else is tasked with decorating a maths department and needs ideas, here’s what I found:
‘Of little practical value’?
Some mathematics, pictured here being hard to illustrate in news coverage
As the heady excitement of the dawn of a forty-eight-Mersenne-prime world dims to a subdued, albeit slightly less factorable, normality, I have taken the opportunity to see what we can learn about the British press’s attitude and ability when it comes to the reporting of big numbers ending in a 1.
Overseas readers may not be aware that the UK’s public service broadcaster, the BBC, is funded by a mandatory annual £145.50 tax on all television-owning households. Therefore, it would be disappointing if some of these funds were not channeled into reporting the discovery in at least five or six separately-produced broadcasts across the organisation’s various radio and television outlets.