Conjectures on the distribution behavior of the class numbers of certain real quadratic number fields

Given a random real quadratic field from ${ $\mathbb{Q}$(\sqrt{p},) ~|~ p $\text{ primes}$ }$,theconjecturalprobability$$\mathbb{P}$(h=q)$ that it has class number $q$ is given for all positive odd integers $q$. Some related conjectures of the Cohen-Lenstra heuristic are given here as corollaries. These results suggest that the set of real quadratic number fields may have some natural hierarchical structures.