In a recent press release off the Great Internet Mersenne Prime Search distributed computing project page, it is announced that $$2^{82589933} - 1$$ is the largest known (Mersenne) prime, corresponding to the $51^{\text{st}}$ known even perfect number $$2^{82589932}(2^{82589933} - 1).$$
According to GIMPS' press release:
This is GIMPS' $12^{\text{th}}$ prime discovery between $2^{20000000}-1$ and $2^{85000000}-1$, triple the expected number of new primes. One reason to search for new primes is to match actual results with expected results. This anomaly is not necessarily evidence that existing theories on the distribution of Mersenne primes are incorrect. However, if the trend continues it may be worth further investigation.
Here are my questions:
(1) How is the expected number of new Mersenne primes computed? Is there some underlying statistical model that is used?
(2) What existing theories would be incorrect if there was indeed an anomaly in the distribution of Mersenne primes?
The following question appears to be related but this is not a duplicate of that one.