I am very aware that the equation in the sandbox might just be a pure coincidence...
...but I want to know for sure.
I mean, it was first assumed that $\pi^3$ was so close to $31$ because it was just a coincidence, but there exists an explanation as to why both the values are close (go here). However, it seems like the fact that $e^\pi - \pi$ is so close to $20$ does not have any known slick proofs, and may just be a beautiful coincidence (go here).
So here is the equation I found:
$$2\ln(662+\pi) = 12.99999987854\ldots\simeq 13.$$
Why is the $LHS$ so close to $13$? Is it just a coincidence, or is there some kind of explanation to it?
Thank you in advance.