I asked my programming teacher how to create a Turing Machine that reaches the nth prime.

He thought I was joking.
He was WRONG.

I never make jokes :)



Anyways, to grok how Turing machines, as described in Automata and Computability, by Dexter C. Kozen, work, here are:
- A Turing Machine that accepts if a number n doesn't divide another number m and rejects otherwise.
- A Turing Machine that accepts if n doesn't divide m, or if n=m, and rejects otherwise.
- A Turing Machine that accepts if n is prime, and rejects otherwise.
- A Turing Machine that accepts once it has found the nth prime.

Early versions, deprecated, start with 0.
- A Turing Machine that accepts if a number n doesn't divide another number m and rejects otherwise.
- A Turing Machine that detects whether a number >=2 is prime.