Incoming links: Erdős' conjecture on powers of 2
Given stuff like arxiv.org/pdf/2107.12475.pdf on Erdős' conjecture on powers of 2, it feels like this one will be somewhere close to computer science/Halting problem issues than number theory. Who knows. This is suggested e.g. at The Busy Beaver Competition: a historical survey by Pascal Michel.
bbchallenge.org/story#what-is-known-about-bb lists some (all?) cool examples,
- BB(15): Erdős' conjecture on powers of 2, which has some relation to Collatz conjecture
- BB(27): Goldbach's conjecture
- BB(744): Riemann hypothesis
- BB(748): independent from the Zermelo-Fraenkel axioms
- BB(7910): independent from the ZFC
wiki.bbchallenge.org/wiki/Cryptids contains a larger list. In June 2024 it was discovered that BB(6) is hard.