BB(10) > Graham's Number
A technical post discusses a new record for the Busy Beaver function (BB(10)), demonstrating a machine that exceeds the growth rate of previous champions. The author details the mathematical proof and the state-based logic used to achieve this result.
Why it matters
This represents a significant milestone in theoretical computer science and the study of non-computable functions.
1RB0RA_1LC1LF_1RD0LB_1RA1LE_1LI0LC_0RG1LD_1RH1LG_1LC0RG_0LJ0LI_1RZ0LC Below we call this machine n1 . It halts from the blank tape, its exact score is proved in Coq, and the score lies between two values of f_(ω+1). The current BB(10) champion has the published bound f_ω(f_ω(25)), at level ω of the fast-growing hierarchy. n1 beats it and moves BB(10) to level ω+1. Written 2026-10-08.
Where it comes from. States A–H form an 8-state machine that we call the base machine . It agrees with the BB(8) record 1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_1LC0RH_1RG1LF ( ../BB8/ ) on states A–E. It runs the same digit-list computation as the record, which is the BB(7) champion's program with 36 digits. n1 keeps the base machine, sends its halting transition E0 to a new state I, and adds the states I and J.
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