I must admit, I haven’t done very much studying at all over the last couple of weeks. I can’t seem to gather up the motivation to finish Unit AA1, knowing that I’ll probably have to go through the entire unit again next year once the Analysis Block A assignment(s) is/are actually due. Instead I’ve been reading Marcus du Sautoy’s *The Music of the Primes*, and falling in love with prime numbers!

A couple of years ago I attempted to read a different book about the Riemann Hypothesis – I think it was *Prime Obsession* – and I just couldn’t get into it, so I was half-expecting to find myself bored by *The Music of the Primes*. Thankfully it was much a more compelling read than I anticipated! Or perhaps I’m just better equipped to understand the appeal of the primes these days.

*The Music of the Primes* is a really enjoyable book, and the only criticism I’ve got is that some of the material was quite familiar to me – the bit about cicadas and their prime-numbered breeding cycles, for instance – so perhaps if you’re a seasoned reader of popular maths books then you might find *The Music of the Primes* a bit boring. But otherwise, I’d recommend it to anyone interested in primes and their mysteries.

For me, the main attraction of prime numbers is that they are fundamental, and at the same time infinite; it seems odd that there are an infinite number of the building blocks out of which the integers are made. Imagine if there were an infinite number of chemical elements! One of my favourite daydreams is imagining the primes stretching out across the far reaches of the real number line, getting bigger and bigger, but more and more sparsely dotted around the line – on and on forever!

The other thing I like about primes is the fact that they’re so important in cryptography – it amuses me that the study of prime numbers has such big practical applications, and I suppose it goes to show that seemingly abstract and academic topics can yield unexpected concrete benefits. Although of course, not everything humans have used prime numbers for could be described as beneficial.

I wonder what the practical applications of group theory are? The next book on my reading list is *Finding Moonshine*, also by Marcus du Sautoy, so hopefully I’ll find out soon enough!

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