Let $X$ be a smooth algebraic variety over $\mathbb{C}$ and consider the derived category $\mathcal{C}=D_h^b(\mathcal{D}_X)$ of bounded complexes of $\mathcal{D}_X$-modules with holonomic cohomology.

The category $\mathcal{C}$ is triangulated (/stable $\infty$-) symmetric monoidal and so it makes sense to ask about its prime spectrum (the collection of all prime ideal thick subcategories).

What is the prime spectrum of $\mathcal{D}_X$? If this is too difficult/general, are there any specific $X$ for which this is known?

Let $X$ be a smooth algebraic (/projective if it simplifies things considerably) variety over $\mathbb{C}$ and consider the derived category $\mathcal{C}=D_h^b(\mathcal{D}_X)$ of bounded complexes of $\mathcal{D}_X$-modules with holonomic cohomology.

The category $\mathcal{C}$ is triangulated (/stable $\infty$-) symmetric monoidal and so it makes sense to ask about its prime spectrum (the collection of all prime ideal thick subcategories).

What is the prime spectrum of $\mathcal{C}$? If this is too difficult/general, are there any specific $X$ for which this is known?