$d\in\Bbb N$ is an idoneal integer if $N\in\Bbb N_{>1}$ can be written uniquely as $N=x^2\pm dy^2$ then $N=2^mp^n$ where $p$ is odd prime and $n\geq0$ and $m\geq0$ holds.

Let the $65$ known idoneal integers be $d_1,\dots,d_{65}$. Let set of primes that can be represented by $d_i$ be $\mathcal P_i$.

Is there an $N_0\in\Bbb N$ such that $\bigcup_{i\in\{1,\dots,65\}}\mathcal P_i$ contain all the primes above $N_0$?

If not what classes of primes are missed out?