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Watch this bold decision-maker score 100 at the “is this prime?” game

Fan of the site Ravi Fernando has written in to tell us about his high score at the “is this prime?” game: a cool century!

I’ve been a fan of your “Is this prime?” game for a while, and after seeing your blog post from last May, I thought I’d say hi and send you some high scores.  Until recently, my record was 89 numbers (last March 12), which I think may be the dot in the top right of your “human scores” graph.  But I tried playing some more a couple weeks ago, and I found I can go a little faster using my computer’s y/n buttons instead of my phone’s touch screen.  It turns out 100 numbers is possible!

Watch in amazement:

But, to the delight of prime fans everywhere, he didn’t stop there:

Today I even got 107 – good to have a prime record again.

Well done, Ravi!

Now is a good time to point out that the data on every attempt ever made at the game is available to download, in case you want to do your own analysis: at time of writing, there have been over 625,000 attempts, and 51 is still the number that catches people out the most.

The magic number 25641

Reader of the site Bhaskar Hari Phadke has written in to tell us this fun fact about the number $25641$. It’s easier to show than to describe, so here goes:

\begin{align}
25641 \times \color{blue}{1} \times 4 &= \color{blue}{1}02564 \\
25641 \times \color{blue}{2} \times 4 &= \color{blue}{2}05128 \\
25641 \times \color{blue}{3} \times 4 &= \color{blue}{3}07692 \\
25641 \times \color{blue}{4} \times 4 &= \color{blue}{4}10256 \\
25641 \times \color{blue}{5} \times 4 &= \color{blue}{5}12820 \\
25641 \times \color{blue}{6} \times 4 &= \color{blue}{6}15384 \\
25641 \times \color{blue}{7} \times 4 &= \color{blue}{7}17948 \\
25641 \times \color{blue}{8} \times 4 &= \color{blue}{8}20512 \\
25641 \times \color{blue}{9} \times 4 &= \color{blue}{9}23076
\end{align}

A good one to challenge a young person with.

I did a little bit of Sloanewhacking and found a couple of sequences containing $25641$ which almost, but don’t quite, describe this property. So, semi-spoiler warning: you might enjoy A256005 and A218857. I’d like to come up with the ‘magic number’ which looks the least like it’ll have this property – any ideas?

Thanks, Bhaskar!

“π – It’s Complicated” – a talk I gave on Pi Day 2016 at Ustinov College Café Scientifique

I was invited to give a talk for Ustinov College’s Café Scientifique on π Day this year. The turnout wasn’t great and I put quite a bit of effort into the slides, so I wanted to put it online. I’ve finally got hold of the recording, so here it is. Unfortunately they didn’t set the camera’s exposure properly, making the screen illegible, so you’ll probably want to follow along with the slides in another window.

I tried to come up with a way of writing today’s date as a multiple of π Day, but couldn’t make it work. However, I did realise that Halloween (31/10) is the best approximation to π between now and the next π day (I think). Sπooky!

The world’s smallest Rubik’s cube is 5.6mm wide and absolutely adorable

I just found this video of a very focused man showing off a teeny tiny Rubik’s cube. It’s 5.6mm on each side, which apparently makes it the smallest in the world, beating some relatively gigantesque efforts of 6mm and larger.

Watch this video; I’ll warn you now that the squee factor gives way to some very dry detail quite quickly.

The cube was made by Tony Fisher, by filing down a 3D-printed 6mm cube. I hadn’t heard of Tony before, which surprises me – his site is full of all sorts of incredible twisty puzzles.

Do you use mixed fractions?

I’m at the MATRIX conference in Leeds, where I’ve just been talking to Adam Atkinson. He told me that he’s trying to compile a definitive list of countries that don’t use mixed fractions.

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.

Integer Sequence Reviews: A075771, A032799, A002717

It’s been almost two years since I last sat down with my friend David Cushing and did what God put us on this Earth to do: review integer sequences.

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.