BB(2,4)
BB(2,4) was unofficially found to be 3,932,964 on April 10, 2023 by the bbchallenge project, when deciders made for solving BB(5) eliminated the last BB(2,4) holdouts. The champion machine M, with S(M) = 3,932,964 and Σ(M) = 2,050, was found by Terry and Shawn Ligocki in February 2005.
Work formalizing this result is ongoing.
History
Brady found a steps and ones champion in 1988, establishing S(2,4) ≥ 7195 and Σ(2,4) ≥ 90.[1]
Champions
S(2,4) = 3,932,964 and there is only one shift champion (in TNF):
- 1RB2LA1RA1RA_1LB1LA3RB1RH leaves 2050 ones (a ones champion)
Σ(2,4) = 2050
- 1RB2LA1RA1RA_1LB1LA3RB1RH runs for 3,932,964 steps (a steps champion)
Enumeration
The top longest running BB(2,4) TMs (in TNF-1RB) are:
Standard Format Steps Σ 1RB2LA1RA1RA_1LB1LA3RB1RH 3932964 2050 1RB3LA1LA1RA_2LA1RH3RA3RB 7195 90 1RB3LA1LA1RA_2LA1RH3LA3RB 6445 84 1RB3LA1LA1RA_2LA1RH2RA3RB 6445 84 1RB2RB3LA2RA_1LA3RB1RH1LB 2351 60
- ↑ Brady A.H. (1988) The busy beaver game and the meaning of life in: The Universal Turing Machine: A Half-Century Survey, R. Herken (Ed.), Oxford University Press, 1988, 259-277.