  Sondow et al have studied Ramanujan primes (RPs) and observed numerically
that, while half of all primes are RPs asymptotically, one obtains runs of
consecutives RPs (resp. non-RPs) which are statistically significantly longer
than one would expect if one was tossing an unbiased coin. In this discussion
paper we attempt a heuristic explanation of this phenomenon. Our heuristic
follows naturally from the Prime Number Theorem, but seems to be only partly
satisfactory. It motivates why one should obtain long runs of both RPs and
non-RPs, and also longer runs of non-RPs than of RPs. However, it also suggests
that one should obtain longer runs of RPs than have so far been observed in the
data, and this issue remains puzzling.
