Conjecture reduction to a halting problem by 
Ciro Santilli 34 Updated 2024-12-15 +Created 1970-01-01
Ciro Santilli 34 Updated 2024-12-15 +Created 1970-01-01bbchallenge.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.