Carnival of Mathematics #157

I checked and it turns out 157 is a prime number. As is its reverse, 751. It looked prime but there are some tricky ones out there that are designed to catch you out. It turns out 157 is actually a sexy prime, this is when n and n+6 are both prime. In fact it is part of a sexy prime triplet; 151, 157 and 163 are all prime.

In researching this I found the neat little proof about the only sexy prime quintuplet:

In an arithmetic progression of five terms with common difference 6, one of the terms must be divisible by 5, because the two numbers are relatively prime. Thus, the only sexy prime quintuplet is (5,11,17,23,29); no longer sequence of sexy primes is possible.

I also discovered that 157 is the smallest three-digit prime that produces five other primes by changing only its first digit and it is palindromic in 2 different bases. Nice!

Anyway, on to the amazing mathsy things that people have been writing about this month...

Firstly on his own blog, John D Cook wrote about posit numbers, a new way to represent real numbers for computers and an alternative to the standard IEEE floating point formats. In Anatomy of a posit number John outlines the interpretation of their bits, and discusses their dynamic range and precision.

On Not Even Wrong, Peter Woit writes about a selection of maths news.  This includes a note that Tom Lehrer turns 90 this month. A perfect excuse to re-visit some of his best songs!

For anyone on twitter you need to be following the tilingbot. A twitter bot creating a random 2-dimensional tiling once a day, by Roice Nelson. Absolutely beautiful.

Mark Dominus writes on The Universe of Discourse about some thoughts on arithmetic sequences, Lower mathematics solves an easy problem. I always love reading about how other people approach mathematical problems, particularly when it is a topic that they may consider elementary but are exploring from a new perspective or with new insight.

Evelyn Lamb writes So Long and Thanks for All the Blogs on the AMS blog. It is her last post though the blog will continue with Anna Haensch in charge. Evelyn includes links to her 6 favourite blog posts from the AMS blog and also a list of her favourite blogs that she follows.

Simon Gregg has been Exploring the Golden Ratio on Seek Echo. He is using Isotiles, a set of isosceles triangles with side ratios 1:ϕ. I'm tempted to get myself a set...

Katie Steckles has written about the winner of the Abel prize 2018 , Robert Langlands on the Mathematik section of the Spektrum blog. "Langlands was a pioneer of this kind of thinking. His work in the 1960s laid the foundation for an entire field of study, and he deserves this recognition for his incredible insights." His work is worth reading about.

Also check out Vincent's new game of heats Card-iac:
Finally Christian L-P has been at it again, check out this nifty web page that splits any number into 3 or fewer palindromic numbers!

Next months Carnival of Mathematics will be hosted by Paul at The Aperiodical.

Here are links if you wish to submit suggestions for next month or find previous issues of Carnival of Mathematics.