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, has S(M) = 3,932,964 and Σ(M) = 2,050.

History

• Brady found a steps and ones champion in 1988, establishing S(2,4) ≥ 7195 and Σ(2,4) ≥ 90.
• Terry and Shawn Ligocki found the champion in 2005 but they did not prove it was BB(2,4).

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