# Does Mihailescu's theorem use the infinitude of primes?

• A
DaTario
TL;DR Summary
Hi all,
I would like to know if in proving the Catalan's conjecture Preda Mihailescu used the infinitude of primes.
Hi all,
I would like to know if in proving the Catalan's conjecture Preda Mihailescu used the infinitude of primes.

Best wishes,
DaTario

Mentor
2021 Award
Do you have a reference? I guess not many people have actually read the proof. Proofs of this kind often prove upper bounds for possible solutions and check the ones below. The infiniteness of primes is so deeply woven into number theory, that it is probably impossible to figure out which theorems it is actually a necessary part of. Nobody will ever have bothered otherwise.

DaTario