  The author has previously extended the theory of regular and irregular primes
to the setting of arbitrary totally real number fields. It has been conjectured
that the Bernoulli numbers, or alternatively the values of the Riemann zeta
function at odd negative integers, are evenly distributed modulo p for every p.
This is the basis of a well-known heuristic given by Siegel for estimating the
frequency of irregular primes. So far, analyses have shown that if Q(\sqrt{D})
is a real quadratic field, then the values of the zeta function
\zeta_{D}(1-2m)=\zeta_{Q(\sqrt{D})}(1-2m) at negative odd integers are also
distributed as expected modulo p for any p. We use this heuristic to predict
the computational time required to find quadratic analogues of irregular primes
with a given order of magnitude. We also discuss alternative ways of collecting
large amounts of data to test the heuristic.
