Definition: A number $$n = \sum_{i = 0}^{k} d_ib^i$$ is called a Cooper number in base $b$, if $$\pi(n) = \prod_{i = 0}^k d_i$$ and $$\pi(\textrm{rev}(n)) = \textrm{rev}(\pi(n)),$$ where $\pi(n)$ is the prime counting function and $\textrm{rev}(n)$ results from reversing the digits of $n$, that is, $$\textrm{rev}(n) = \sum_{i = 0}^{k} d_{k - i} b^i.$$
A Cooper number $n$ is called a Cooper prime if $n$ and $\textrm{rev}(n)$ are prime numbers.
The well known example is $73$ in base $10$, with $\pi(73) = 21$ and $\pi(37) = 12$. It is known that in base $10$ the only Cooper prime is $73$.
Other examples of a Cooper number are $8 = 22_3$ in base $3$, $27 = 33_8$ in base $8$ and $3087 = 21 \times 146 + 21$ in base $146$, since $\pi(3087) = 441 = 21^2$.
I was not able to find any more, but beside $73$ in base $10$ there is a pattern with $8$, $27$ and $3087 $are palindromic in the corresponding base.
Any idea how to prove that there are no more Cooper numbers?