Asymptotic ratio of non-primonumerophobic and digit-pattern sequences

Let $A267013(d)$ denote the number of non-primonumerophobic digit patterns of length $d$, and let $A164864(d)$ denote the total number of available digit patterns of length $d$. Asymptotic ratio conjecture. As $d\rightarrow\fty$, the ratio of these sequences satisfies

$$\frac{A267013(d)}{A164864(d)}\sim\frac{9\cdot9!}{d\ln 10}.$$

The preceding combinatorial estimate yields the same asymptotic expression heuristically, but the supplied source does not establish the corresponding asymptotic for the exact sequences.