The middle-third Cantor set C3 is a fractal consisting of all the points in
[0,1] which have non-terminating base-3 representations involving only the
digits 0 and 2. I prove that all prime numbers p > 3 whose reciprocals belong
to C3 must be base-3 repunit primes, and, conversely, that the reciprocals of
all base-3 repunit primes must be in C3. This one-one correspondence appears to
be unique to the base-3 case.