Closing in on the twin prime conjecture (Quanta) - "Just months after Zhang announced his result, Maynard has presented an independent proof that pushes the gap down to 600. A new Polymath project is in the planning stages, to try to combine the collaboration's techniques with Maynard's approach to push this bound even lower." [more inside]
What is the smallest prime? "It seems that the number two should be the obvious answer, and today it is, but it was not always so. There were times when and mathematicians for whom the numbers one and three were acceptable answers. To find the first prime, we must also know what the first positive integer is. Surprisingly, with the definitions used at various times throughout history, one was often not the first positive integer (some started with two, and a few with three). In this article, we survey the history of the primality of one, from the ancient Greeks to modern times. We will discuss some of the reasons definitions changed, and provide several examples. We will also discuss the last significant mathematicians to list the number one as prime."
New math theories reveal the nature of numbers [1,2] - "We prove that partition numbers are 'fractal' for every prime. These numbers, in a way we make precise, are self-similar in a shocking way. Our 'zooming' procedure resolves several open conjectures, and it will change how mathematicians study partitions." (/.|via) [more inside]
Joe Palca, a science correspondent for NPR's Morning Edition, was meditating on the best way to convey the magnitude of the world's largest known prime number, 243112609-1. He contacted H&FJ at Typography.com to discuss the implications of typesetting a number with more than twelve million digits. Crunching of numbers and fonts ensued.
In September 2006 the largest known prime number, a 9.8 million digit number, was discovered. If you find one over ten million digits you can win US$100,000 (of which you get to keep $50,000). No maths is required - just download the software and you're away. Warning: it takes about a month to run one primality check so some patience is required. Look out though Cooper and Boone look like they might beat you to it.
Prime Time. A prime is a whole number divisible only by itself and 1. In Aesthetics of the prime sequence one can hear primes, view primes (here also) and test for primes. Quite interesting and not just for math geeks...