Thanks! I am a mathematician, so am fine with the discussion of the 𝜁 function. I get the impression that de Sautoy is overselling the connexion a little bit in his zeal to make an analogy, but (1) I don't know the area, and so shouldn't really comment, and (2) it's interesting even if it's oversold.
http://seedmagazine.com/content/article/prime_numbers_get_hi... Nice summary: http://carbonatoms.wordpress.com/2009/03/13/prime-numbers-ar...
Primes appear to be zeroes of the Reimann Zeta Function. Nature loves minimizing energy, so there might be some reason the Zeta Function models how atoms behave. Then, primes are the most "stable orbits" or have a similarly useful property.
Super high level, but I think it's interesting.