In 1984, Cohen and Lenstra made a number of conjectures regarding the
class groups of quadratic fields. In particular, they predicted the proportion
of real quadratic fields with class number divisible by an odd prime. We
numerically investigate the difference between reality and these predictions.
Using 4 million data points, we perform a curve fitting of the difference
with a monomial term and demonstrate that there is reason to believe the
term can be effectively approximated within the scope of our data set for
odd primes less than 30. We use cross-validation to show that including our
monomial term as a secondary term to the original conjecture reduces the overall
error.
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