Read A Number Theorist Who Solves the Hardest Easy Problems by Erica KlarreichErica Klarreich (Quanta Magazine)
In his rapid ascent to the top of his field, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.
A paragraph or two on some of the more technical aspects would have been better than some of the hero-worship and seeming lone-genius narrative that was developed here. Use the particulars about the person to develop some interest in the mathematics and its history.

👓 How to Memorize the Largest Known Prime | Scientific American Blog Network

Read How to Memorize the Largest Known Prime (Scientific American Blog Network)
It may seem daunting to memorize a 24 million digit number, but with these tips, you'll be well on your way

👓 News re proofs of the ABC conjecture & Riemann Hypothesis | John D. Cook

Read News re proofs of the ABC conjecture & Riemann Hypothesis by John D. Cook (johndcook.com)
There have been a couple news stories regarding proofs of major theorems. First, an update on Shinichi Mochizuki’s proof of the abc conjecture, then an announcement that Sir Michael Atiyah claims to have proven the Riemann hypothesis.

👓 Kaisa Matomäki Dreams of Primes | Quanta Magazine

Read Kaisa Matomäki Dreams of Primes by Kevin Hartnett (Quanta Magazine)
Kaisa Matomäki has proved that properties of prime numbers over long intervals hold over short intervals as well. The techniques she uses have transformed the study of these elusive numbers.

Primes as a Service on Twitter

Our friend Andrew Eckford has spent some time over the holiday improving his Twitter bot Primes as a Service. He launched it in late Spring of 2016, but has added some new functionality over the holidays. It can be relatively handy if you need a quick answer during a class, taking an exam(?!), to settle a bet at a mathematics tea, while livetweeting a conference, or are hacking into your favorite cryptosystems.

General Instructions

Tweet a positive 9-digit (or smaller) integer at @PrimesAsAService. It will reply via Twitter to tell you if the number prime or not.

Some of the usable commands one can tweet to the bot for answers follow. (Hint: Click on the buttons with the tweet text to auto-generate the relevant Tweet.)

If you ask about a prime number with a twin prime, it should provide the twin.

Pro tip: You should be able to drag and drop any of the buttons above to your bookmark bar for easy access/use in the future.

Happy prime tweeting!