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I'm one of those guys who didn't necessarily pay a lot of attention to maths in college - not that I don't see the value in it, but it is certainly not a core interest. However, I've been slowly getting more and more into maths and the science of primes. So this post (and the questions the Ulam spiral asks) strike me at the worst of times and the best of times.

If you're at least a bit like me (no deep knowledge of maths, but growing curiosity) I recommend checking out BBC's recent documentary on primes, called 'The Music of the Primes'. It'll spark your interest, and it'll make you want to dig a little deeper.

if you've ever prepared for a standardized quant test like the GMAT it immediately becomes apparent how useful even a basic understanding of primes can be. being able to manipulate primes at even the superficial level required (to do well) by these exams gives great insight and appreciation for the power/beauty of prime numbers. it really opened my eyes to mathematics in general, and i wish it were an education/perspective i'd been given as a child rather than a young adult. (I realize the GMAT is likely anathema to this forum so i hesitate in mentioning it, but the result of my preparation was some surprisingly useful insight in these regards...)

I'd put myself in the same category, math-curious. I missed the TV series, but bought the book instead: http://www.musicoftheprimes.com/thebook.htm It's a good read.

BTW I hadn't seen that website until I went looking for a URL for the book just now. The site seems to have some pretty interesting material in its own right too.

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