Champions: Difference between revisions
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|[[BB(7)]] | |[[BB(7)]] | ||
|<math> > 10 \uparrow\uparrow | |<math> > 10 \uparrow\uparrow 286 </math> | ||
|{{TM| | |{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ|halt}} | ||
|[https://discord.com/channels/960643023006490684/1369339127652159509/ | |[https://discord.com/channels/960643023006490684/1369339127652159509/1370683302176096347 Terry Ligocki in 2025] | ||
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Revision as of 10:45, 10 May 2025
Busy Beaver Champions are the current record holding Turing machines who maximize a Busy Beaver function. In this article we focus specifically on the longest running TMs. Some have been proven to be the longest running of all (and so are the ultimate champion) while others are only current champions and may be usurped in the future. For smaller domains, Pascal Michel's website is the canonical source for Busy Beaver champions and the History of Previous Champions.
2-Symbol TMs
Rows are blank if no champion has been found which surpasses a smaller size problem. Take also note that the Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f_{x}(n) } used in the lowerbounds represent the Fast Growing Hierarchy. Note that most champions above 6 states are self-reported and have not been independently verified.
| Runtime | Champions | Discovered By | Verification | |
|---|---|---|---|---|
| BB(2) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 6 } | 1RB1LB_1LA1RZ (bbch) 1RB0LB_1LA1RZ (bbch) 1RB1RZ_1LB1LA (bbch) 1RB1RZ_0LB1LA (bbch) 0RB1RZ_1LA1RB (bbch)
|
Tibor Radó | Direct Simulation |
| BB(3) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 21 } | 1RB1RZ_1LB0RC_1LC1LA (bbch)
|
Proven by Shen Lin | Direct Simulation |
| BB(4) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 107 } | 1RB1LB_1LA0LC_1RZ1LD_1RD0RA (bbch)
|
Allen Brady | Direct Simulation |
| BB(5) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 47\,176\,870 } | 1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA (bbch)
|
Heiner Marxen & Jürgen Buntrock in 1989 | Direct Simulation |
| BB(6) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > 10 \uparrow\uparrow 15 } | 1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LF0RB_0RC0RE (bbch)
|
Pavel Kropitz in 2022 | Analysis by Shawn Ligocki |
| BB(7) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > 10 \uparrow\uparrow 286 } | 1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ (bbch)
|
Terry Ligocki in 2025 | |
| BB(8) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > 2 \uparrow^5 4 > f_6(2) } | 1RH1RF_0LC0LH_0RD1LC_0RE1RA_1RB1RE_1RZ1RG_1RF0RE_1LB1LH (bbch)
|
Racheline in 2024 | |
| BB(9) | 1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_1LB0LH (bbch)
|
Jacobzheng in 2024 | ||
| BB(10) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > f_\omega^2(25) } | 1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_0LF0LJ_1LH0LJ (bbch)
|
Racheline in 2024 | |
| BB(11) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > f_\omega^2(2 \uparrow\uparrow 12) > f_\omega^2(f_3(9)) } | 1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RZ0LI_0LD1LE (bbch)
|
Racheline in 2024 | |
| BB(12) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > f_\omega^4(2 \uparrow\uparrow\uparrow 4-3) > f_\omega^4(f_4(2)) } | 0LJ0RF_1LH1RC_0LD0LG_0RE1LD_1RF1RA_1RB1RF_1LC1LG_1LL1LI_1LK0LH_1RH1LJ_1RZ1LA_1RF1LL (bbch)
|
Racheline in 2024 | |
| BB(13) | ||||
| BB(14) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > f_{\omega + 1}(65\,536) > g_{64} } | 1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RL0LI_0LL1LE_1LM1RZ_0LN1LF_0LJ--- (bbch)
|
Racheline in 2024 | |
| BB(15) | ||||
| BB(16) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > f_{\omega + 1}(2 \uparrow\uparrow\uparrow\uparrow 2 \uparrow\uparrow\uparrow\uparrow 9) } | Daniel Nagaj in 2021 | Analysis by Shawn Ligocki | |
| BB(17) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > f_{\omega + 1}(f_\omega(60)) } | User:Jacobzheng/BB(17) | Jacobzheng in 2024 | |
| BB(18) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > f_{\omega + 1}(f_\omega^2(60)) } | User:Jacobzheng/BB(18) | Jacobzheng in 2024 | |
| BB(19) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > f_{\omega + 1}^3(f_\omega(60)) } | User:Jacobzheng/BB(19) | Jacobzheng in 2024 | |
| BB(20) | Racheline in 2024 | |||
| BB(21) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > f_{\omega^2}^2(4 \uparrow\uparrow 341) } | Racheline in 2024 | ||
| BB(40) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > f_{\omega^\omega}(75\,500) } | User:Jacobzheng/BB(40) | Jacobzheng in 2024 | |
| BB(41) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > f_{\omega^\omega}^4(32) } | User:Jacobzheng/BB(41) | Jacobzheng in 2024 | |
| BB(51) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > f_{\varepsilon_0 + 1}(8) } | Racheline in 2024 |
3-Symbol TMs
| Runtime | Champions | Discovered By | Verification | |
|---|---|---|---|---|
| BB(2,3) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 38 } | 1RB2LB1RZ_2LA2RB1LB (bbch)
|
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| BB(3,3) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > 10^{17} } | 0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC (bbch)
|
||
| BB(4,3) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > 2 \uparrow\uparrow\uparrow 2^{2^{32}}} | 0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD (bbch)
|
4-Symbol TMs
| Runtime | Champions | Discovered By | Verification | |
|---|---|---|---|---|
| BB(2,4) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 3\,932\,964 } | 1RB2LA1RA1RA_1LB1LA3RB1RZ (bbch)
|
Shawn & Terry Ligocki in 2005 | Pascal Michel, Hiener Marxen, Allen Brady |
| BB(3,4) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > 2 \uparrow^{15} 5 } | 1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC (bbch)
|
5-Symbol TMs
| Runtime | Champions | Discovered By | Verification | |
|---|---|---|---|---|
| BB(2,5) | 1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ (bbch)
|
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| BB(3,5) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > f_\omega(2 \uparrow^{15} 5) > f_\omega^2(15) } | 1RB3LB4LC2RA4LB_2LC3RB1LC2RA1RZ_3RB1LB3LC2RC4LC (bbch)
|
6-Symbol TMs
| Runtime | Champions | Discovered By | Verification | |
|---|---|---|---|---|
| BB(2,6) |