Busy Beaver Hunters Reach Numbers That Overwhelm Ordinary Math | Quanta Magazine
The quest to find the longest-running simple computer program has identified a new champion. It’s physically impossible to write out the numbers involved using standard mathematical notation.
Hasnain says:
“This new result is still just a lower limit on BB(6) — the true value could be even higher. Busy beaver hunters don’t expect to have a definitive answer anytime soon. The first sign of trouble was a monstrous six-rule Turing machine that the team has named Antihydra (opens a new tab), discovered by mxdys last year.
Antihydra almost certainly never halts. But researchers haven’t been able to prove it. And there’s a good reason for that: A busy beaver hunter who goes by Racheline has shown that the question of whether Antihydra halts is closely related to a famous unsolved problem in mathematics called the Collatz conjecture. Since then, the team has discovered many other six-rule machines with similar characteristics. Slaying the Antihydra and its brethren will require conceptual breakthroughs in pure mathematics.”
Posted on 2025-08-24T04:59:58+0000