Barry Mazur and William Stein are working on a volume entitled "
Primes" to explain the Riemann Hypothesis to a larger audience. A working (very lay-friendly) draft of it is available for free download here!:
http://modular.math.washington.edu/rh/
On the same page, you can also view an hour-long Fora/TV talk of Mazur explaining, how to go about explaining the RH.
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