Find the number x that satisfies two interesting properties.

A mad robot sets off on a journey mindlessly following a set of instructions. Where will it explode?

Sharpen that wooden stake!

Which gives a tighter fit: a square peg in a round hole or a round peg in a square hole?

How many prisoners escape after visits from wardens?

The n-th birthday of a very famous mathematician coincides with a year that corresponds to the (n+1)st prime number. Who is this mathematician?