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by Ciro Santilli (@cirosantilli, 37)

Turing machine that halts if and only if Collatz conjecture is false

 ... Decision problem Halting problem Busy beaver Busy beaver scale Automated theorem proving by halting problem reduction Conjecture reduction to a halting problem
 0 By others on same topic  0 Discussions  Updated 2025-05-26  +Created 1970-01-01  See my version
Tags: Collatz conjecture
mathoverflow.net/questions/309044/is-there-a-known-turing-machine-which-halts-if-and-only-if-the-collatz-conjectur suggests one does not exist. Amazing.
Intuitively we see that the situation is fundamentally different from the Turing machine that halts if and only if the Goldbach conjecture is false because for Collatz the counter example must go off into infinity, while in Goldbach conjecture we can finitely check any failures.
Amazing.

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