User:Azerty/Busy Beaver Functions: Difference between revisions

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|[[BB(2,6)]]
|[[BB(2,6)]]
|<math>> 10 \uparrow\uparrow 10 \uparrow\uparrow 10^{10^{115}}</math><ref name=":1">S. Ligocki, "[https://www.sligocki.com/2023/05/20/bb-2-6-p3.html BB(2,6) > 10↑↑10↑↑10↑↑3]". Blog post, 2023. Accessed 15 August 2025.</ref>
|<math>> 10 \uparrow\uparrow 10 \uparrow\uparrow 10^{10^{115}}</math>
|{{TM|1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA|halt}}
|{{TM|1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA|halt}}
|-
|-
|[[BB(6)]]
|[[BB(6)]]
|<math>> 10 \uparrow\uparrow 10 \uparrow\uparrow 10 \uparrow\uparrow 8</math><ref name=":1" />
|<math>> 10 \uparrow\uparrow 10 \uparrow\uparrow 10 \uparrow\uparrow 8</math>
|{{TM|1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE|halt}}
|{{TM|1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE|halt}}
|-
|-
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|[[BB(3,4)]]
|[[BB(3,4)]]
|<math>> 10 \uparrow^{15} 4</math><ref name=":0">S. Ligocki. "BB(3,4) > Ack(14)." https://www.sligocki.com/2024/05/22/bb-3-4-a14.html  Blog post, 2024. Accessed 15 August 2025.</ref>
|<math>> 10 \uparrow^{15} 4</math>
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|{{TM|1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC|halt}}
|}
|}

Revision as of 10:45, 4 December 2025

This is a list of Busy Beaver functions for Turing machines and other simple Turing-complete systems and their current lower bounds.

All functions here grow uncomputably fast like the original Busy Beaver function. There is no function that grow much faster like the Beeping Busy Beaver function here.

I will add more functions soon.

Turing Machines

Function Lower Bound Champion
BB(2) 6 1RB1LB_1LA1RZ (bbch)
BB(3) 21 1RB1RZ_1LB0RC_1LC1LA (bbch)
BB(2,3) 38 1RB2LB1RZ_2LA2RB1LB (bbch)
BB(4) 107 1RB1LB_1LA0LC_1RZ1LD_1RD0RA (bbch)
BB(2,4) 3,932,964 1RB2LA1RA1RA_1LB1LA3RB1RZ (bbch)
BB(5) 47,176,870 1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA (bbch)
BB(3,3) >1.191×1017 0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC (bbch)
BB(2,5) >1010103314360 1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ (bbch)
BB(2,6) >10↑↑10↑↑1010115 1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA (bbch)
BB(6) >10↑↑10↑↑10↑↑8 1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE (bbch)
BB(4,3) >10↑310↑310↑31028 1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD (bbch)
BB(7) >10↑1110↑104 1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch)
BB(3,4) >10↑154 1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC (bbch)
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