Here are some nice number facts and tricks you can try out on your friends. They will work without understanding how, but with a little investigation you should be able to figure out how each one works.
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Primes gotta stick together
Update 14/05/2013: The seminar was successful: Zhang announced that his proof has already been refereed for the Annals, and everyone seems happy with it.
Hard Maths news now: there’s a rumour going round that Yitang (Tom) Zhang of the University of New Hampshire reckons he can prove that there are infinitely many different pairs of primes at most 70,000,000 apart.
LMS Popular Lectures 2013: ‘Mathematics in the Courtroom’ and ‘Addictive Number Theory
The London Mathematical Society Popular Lectures for 2013 have been announced. Professor Ray Hill, University of Salford, will talk about ‘Mathematics in the Courtroom’, and Dr. Vicky Neale, University of Cambridge, will give a lecture on ‘Addictive Number Theory’.
On Disreputable Numbers
One would be hard put to find a set of whole numbers with a more fascinating history and more elegant properties surrounded by greater depths of mystery — and more totally useless — than the perfect numbers.
— Martin Gardner
There are countless ways to classify integers. Happy, perfect, friendly, sociable, abundant, extravagant, cute, interesting, frugal, deficient, hungry, undulating, weird, vampire… the list goes on. But how useful are such classifications, beyond their inherent interestingness, and as a hook to get people into number theory?