GoKawiilNew 10-state Turing machine sets BB(10) record, surpasses Graham's number
Researchers have identified a 10-state, 2-symbol Turing machine, dubbed n1, that halts on a blank tape and produces a number of 1s exceeding Graham's number. The machine's exact halting score and its placement at level ω+1 of the fast-growing hierarchy have been formally verified in Coq without relying on any axioms, surpassing the previous BB(10) champion, which sat at level ω.
GoKawiil's interpretation of the reporting above, not reported fact.
The result pushes the known frontier of the Busy Beaver problem for 10-state machines to a new growth-rate level, suggesting that small Turing machines can encode functions of extraordinary scale using relatively modest modifications to existing record-holding programs. Because the proof is machine-checked in Coq, it offers a high degree of confidence that could prompt renewed interest in exploring even larger or more complex small-state machines for future Busy Beaver research.
- A 10-state machine (n1) halts and generates a score proven to exceed Graham's number.
- The machine's score is formally verified in Coq to lie strictly between two values of f_(ω+1) in the fast-growing hierarchy.
- n1 builds on the BB(8) champion machine by adding two new states, surpassing the prior BB(10) record which was at level ω.
Source: github.com, 2026-10-13
Published there as: “BB(10) > Graham's Number”
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