A specific syntax for printing objects of type random-state is not specified. However, every implementation must arrange to print a random state object in such a way that, within the same implementation, read can construct from the printed representation a copy of the random state object as if the copy had been made by make-random-state.
If the type random state is effectively implemented by using the machinery for defstruct, the usual structure syntax can then be used for printing random state objects; one might look something like
#S(RANDOM-STATE :DATA #(14 49 98436589 786345 8734658324 ... ))
where the components are implementation-dependent.