I saw on this website that $7$ is the only prime number followed by $x^3$. What is known about primes followed by $x^n$, for $n>3$? Are there any?
For less than $n=2$, there is clearly $3$ which is followed by $2^2$. That can be narrowed to requiring that for the $x^2$, the x must be even (so that the number it follows is at least odd). Other examples?