Collaborative prime number searching website PrimeGrid has announced its most recent discovery: on 14th September, user Tom Greer discovered a new pair of twin primes (primes which differ by 2), namely:

\[2996863034895 \times 2^{1290000} \pm 1\]

Found using PrimeGrid’s Sophie Germain Prime search, the new discoveries are 388,342 digits long, smashing the previous twin prime record of 200,700 digits.

PrimeGrid is a collaborative project (similar to GIMPS, which searches for specifically Mersenne Primes) in which anyone who downloads their software can donate their unused CPU time to prime searching. It’s been the source of many recent prime number discoveries, including several in the last few months which rank in the top 160 largest known primes.

The University of Tennessee Martin’s Chris Caldwell maintains a database of the largest known primes, to which the new discovery has been added.

Press release from PrimeGrid (PDF)

The List of Largest Known Primes

PrimeGrid website

The new twin primes’ entries on the List of Largest Known Primes: n+1, n-1

The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.

]]>The University of Leicester says it’s facing a big budget deficit, so it’s got to make some cuts. In the current British climate, that’s nothing unusual. However, the university has decided to cut a lot more from the maths department than elsewhere.

The way they’re going to do this is to sack almost everyone, then ask them to re-apply for slightly fewer jobs than there were before. Once it’s all done, 6 of the 21 mathematicians currently working at Leicester will be out of a job.

There’s some speculation that the reason that maths is going to be hit particularly hard is that it didn’t do particularly well in the last iterations of the REF and the National Student Survey.

The Universities and Colleges Union has started a petition against the cuts, disputing the size of the deficit and the need for so many job losses. They’ve written a response laying out their side of the story. The European Mathematical Society has also said it’s very concerned.

Tim Gowers has written a bit more about what he thinks is going on on his blog. As usual, there’s some good discussion in the comments as well.

*via Yemon Choi*

Puzzlebomb is a monthly puzzle compendium. Issue 57 of Puzzlebomb, for September 2016, can be found here:

Puzzlebomb – Issue 57 – September 2016 (printer-friendly version)

The solutions to Issue 57 will be posted at the same time as Issue 58.

Previous issues of Puzzlebomb, and their solutions, can be found at Puzzlebomb.co.uk.

]]>Today my phone told me that the app Photomath has an update and now supports handwriting recognition. This means I can write something like this:

and Photomath does this with it:

Well. My immediate reaction is to be quite terrified. Clearly this is a fantastic technical achievement and a wonderful resource, but my thoughts go straight to assessment. I remember when I heard Wolfram Alpha was released, I was working to input questions a lecturer had written into an e-assessment system and realised that all the questions on the assessment I was inputting could be answered, with zero understanding, by typing them into Wolfram Alpha. Actually, not quite zero understanding, because at least you had to be able to reliably type the question. Now Photomath closes that gap (or will do soon – of course, it’s not yet perfect).

However, a lot of water has passed under the bridge since I was inputting questions into an e-assessment system. I’m a lecturer at Sheffield Hallam University now, where students who don’t arrive knowing about Wolfram Alpha are told about it, because students are encouraged to learn to use any technology available to them. Indeed, this year I was involved with marking a piece of coursework where engineering students were asked to show by hand how they had worked out their solutions and provide evidence that they checked their answer by an alternative method, usually by Wolfram Alpha screenshot.

It if often the case that lecturers use computers when setting assessments (beyond typesetting, I mean), even when they don’t expect students to use them in answering. I asked this question in a survey for my PhD and even about half of people who don’t use e-assessment with their students still use computers when setting questions (to check their answers are correct, perhaps). (Link to PhD thesis, see section 3.4.5 on p. 60.) Perhaps we should encourage our students to embrace technology in the same way.

In the academic year that is about to start, I am to teach on the first year modelling module. This is where our first year mathematics degree students get their teeth into some basic mathematical models, ahead of more advanced modelling modules in the second and final year. If you accept that a lot of mathematics is a process of: understand and formulate the problem, solve it, then translate and understand that solution – then this sort of technology only helps with the ‘solve it’ step. In the case of modelling, taking a real world situation, interpreting that as a mathematical model and extracting meaning from your solution are difficult tasks of understanding which these technologies do not help with, even as they help you get quickly and easily to a solution.

So, should I view Photomath as a terrifying assault on our ability to test students’ ability to apply mathematical techniques? Probably I should view it instead as a powerful tool to add to the mathematician’s toolkit, which hints at a world where handwritten mathematics can be solved or converted to nicely typeset documents, and so allow my students to gravitate from the tedious mechanics of the subject to greater ability to apply and show off their understanding. Probably.

]]>Oh blimey pic.twitter.com/OdKS1MmY1N

— Peter Rowlett (@peterrowlett) September 4, 2016

Here’s a mixed fraction: \[ 2 \frac{2}{3} \]

And here’s a non-mixed fraction: \[ \frac{8}{3} \]

Actually, here’s an interesting fact about that number: \[ 2 \sqrt{ \frac{2}{3} } = \sqrt{ 2 \frac{2}{3} } \]

This only makes sense if you believe in mixed fractions (and unicode character U+2062, “invisible times”)

This is going to be one of those wipe-your-bum-standing-up situations: it’s entirely possible that you can be on either side of this divide and not know the other exists. Apparently, in some countries mixed fractions just don’t exist: an integer written next to a fraction is incorrect.

So, to help Adam on his way, I thought I’d start another in our long-running series of Aperiodical Surveys. Please tell us where you live, and if mixed fractions are OK in your book.

Next week, the British Science Festival will take place in Swansea, in and around the University. Here’s our round-up of all the mathsiest of the maths events taking place during the week. Our own Katie Steckles will be there introducing most of these events, so you might spot her at the front telling you what to do if there’s a fire. You’ll need to register to book tickets, but all the events are free.

Lecture Theatre K, Faraday Building

Suitable for 16+

In 7 dimensions there exist special shapes that may give us the tools to unlock the mysteries of the universe. Looking for this unique geometry is challenging but a possible solution takes inspiration from nature: specifically, bubbles and thermodynamics. **Jason Lotay** takes us on a mathematical journey across multiple dimensions, whilst exploring their role in art, science and popular culture.

Lecture Theatre B, Glyndwr Building

Organised by Swansea University; Suitable for 16+

How can we attempt to predict earthquakes, financial crashes and acts of terrorism? Such events can often seem random but researchers can unpick the underlying complexity using probability models known as Hawkes processes. Join **Alan Hawkes** himself and his collaborator **Maggie Chen** to discover the wide-ranging applications of these mathematical models.

Taliesin Theatre, Taliesin Arts Centre

Suitable for 16+

One of the tools in the disease-fighter’s arsenal is mathematics. How can we measure disease spread? How can a few key people shape an outbreak? Which infections are hardest to control? **Adam Kucharski** shares his experience working to understand new disease threats, from Ebola to pandemic flu.

Lecture Theatre, Wallace Building

Suitable for 16+

Cryptography is the cornerstone of our online security, protecting our email messages, credit card information and medical records. Join mathematician and Advisor to GCHQ **Richard Pinch** to explore security and privacy in an increasingly connected world and find out how new technologies such as quantum computing could threaten our cyber-security.

The Presidential Lecture will be followed by a drinks reception at 17.00 on the Wallace Landing.

Lecture Theatre M, Faraday Building

Suitable for 16+

Sepsis, also known as blood poisoning, kills 40,000 people in the UK each year. Many of those lives could be saved through early diagnosis and treatment. Meet a mathematician and physiologist working together to detect the early stages of sepsis and hear how mathematical methods can help address important health issues.

The festival will be followed by a weekend of activities for children and families, including:

A circus of mathematical activities, games and exhibits, accessible to all ages and designed to take you on a tour of the world of mathematics from the practical to the highly abstract. Mathematics is the language of science and we will show you how mathematical research is pushing forward the frontiers of biology, computing, engineering, medicine, physics and more.

Check the Festival website at britishsciencefestival.org for the full programme.

]]>

The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.

]]>Puzzlebomb is a monthly puzzle compendium. Issue 56 of Puzzlebomb, for August 2016, can be found here:

Puzzlebomb – Issue 56 – August 2016 (printer-friendly version)

The solutions to Issue 56 will be posted at the same time as Issue 58.

Previous issues of Puzzlebomb, and their solutions, can be found at Puzzlebomb.co.uk.

]]>This week I lured David into my office with promises of tasty food and showed him some sequences I’d found. Thanks to (and also in spite of) my Windows 10 laptop, the whole thing was recorded for your enjoyment. Here it is:

I can only apologise for the terrible quality of the video – I was only planning on using it as a reminder when I did a write-up, but once we’d finished I decided to just upload it to YouTube and be done with it.

We reviewed the following sequences:

A075771

Let $n^2 = q \times \operatorname{prime}(n) + r$ with $0 \leq r \lt \operatorname{prime}(n)$; then $a(n) = q + r$.1, 2, 5, 4, 5, 12, 17, 10, 15, 16, 31, 36, 9, 28, 41, 48, 57, 24, 31, 50, 9, 16, 37, 48, 49, 76, 15, 42, 85, 116, 79, 114, 137, 52, 41, 96, 121, 148, 27, 52, 79, 144, 139, 16, 65, 136, 109, 84, 141, 220, 49, 86, 169, 166, 209, 254, 33, 124, 169, 240, 55, 48, 297, 66

A032799

Numbers $n$ such that $n$ equals the sum of its digits raised to the consecutive powers $(1,2,3,\ldots)$0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 89, 135, 175, 518, 598, 1306, 1676, 2427, 2646798, 12157692622039623539

]]>

A002717

$\lfloor n(n+2)(2n+1)/8 \rfloor$0, 1, 5, 13, 27, 48, 78, 118, 170, 235, 315, 411, 525, 658, 812, 988, 1188, 1413, 1665, 1945, 2255, 2596, 2970, 3378, 3822, 4303, 4823, 5383, 5985, 6630, 7320, 8056, 8840, 9673, 10557, 11493, 12483, 13528, 14630, 15790, 17010, 18291, 19635, 21043, 22517