BB(2,4)
BB(2,4) was officially found to be 3,932,964 on August 22, 2024 by the bbchallenge project, when a proof for the BB(2,4) case was added to Coq-BB5 and successfully compiled. 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.
History
- Brady found a steps and ones champion in 1988, establishing S(2,4) ≥ 7195 and Σ(2,4) ≥ 90.[1]
- Terry and Shawn Ligocki found the current champion in 2005.
Champion
S(2,4) = 3,932,964 and Σ(2,4) = 2050 and both are achieved by only one champion (in TNF):
1RB2LA1RA1RA_1LB1LA3RB1RZ(bbch)
Enumeration
The top 20 longest running BB(2,4) TMs (in TNF-1RB) are:
Standard Format Steps Σ 1RB2LA1RA1RA_1LB1LA3RB1RZ 3932964 2050 1RB3LA1LA1RA_2LA1RZ3RA3RB 7195 90 1RB3LA1LA1RA_2LA1RZ3LA3RB 6445 84 1RB3LA1LA1RA_2LA1RZ2RA3RB 6445 84 1RB2RB3LA2RA_1LA3RB1RZ1LB 2351 60 1RB3RA1LA2RB_2LA3LA1RZ1RA 1021 53 1RB3LA1RZ0RB_2LB2LA0LA0RA 1001 26 1RB2LA1RZ3LA_2LA2RB3RB2LB 770 30 1RB2LB1RZ3LA_2LA2RB3RB2LB 708 29 1RB2LA0RB1LB_1LA3RA1RA1RZ 592 24 1RB3LA3RA0LA_2LB1LA1RZ2RA 392 20 1RB3LA1LA1RA_2LA1RZ2RB3RB 376 21 1RB3LA1LA1RA_2LA1RZ0LA3RB 376 21 1RB3LA3RB0LA_2LA1RZ1LB3RA 374 22 1RB1RA1LB0RA_2LA3RB2RA1RZ 335 18 1RB2LA3LA1LB_2LA1RZ2RB0RA 292 18 1RB0RB1RZ0LA_2LA3RA3LA1LB 289 13 1RB1LA1RZ0LB_2LA3RB1RB2RA 283 18 1RB3LA3RA0LA_2LB1LA1RZ3RA 266 19 1RB2RB1RZ1LB_2LA2LB3RB0RB 241 15
For the top 100 halting BB(2,4) TMs, see: https://github.com/sligocki/busy-beaver/blob/main/Machines/bb/2x4.txt
- ↑ 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.