Revision as of 10:48, 17 August 2025

A collection of Busy Beaver Champions including Champions for BB-Adjacent functions. Note that for all functions with the input format f(n,m), n denotes the number of states and m denotes the number of symbols of the relevant Busy Beaver domain. Note that for functions with this input format f(n) = f(n,2).

State-and-Symbol-Limited Busy Beaver functions

Original Busy Beaver Functions

Maximum Shifts Function (S(n,m), also commonly called BB(n,m))

2 Symbols:


	Runtime	Champions
BB(1)	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 1}	`1RZ---` (bbch)
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)
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)
BB(4)	$107$	`1RB1LB_1LA0LC_1RZ1LD_1RD0RA` (bbch)
BB(5)	$47\,176\,870$	`1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA` (bbch)
BB(6)	$>2\uparrow \uparrow 2\uparrow \uparrow 2\uparrow \uparrow 10$	`1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE` (bbch)
BB(7)	$>2\uparrow ^{11}2\uparrow ^{11}3$	`1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF` (bbch)
BB(8)
BB(9)	$>f_{\omega }(f_{9}(2))$	`1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_1LB0LH` (bbch)
BB(10)	$>f_{\omega }^{2}(25)$	`1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_0LF0LJ_1LH0LJ` (bbch)
BB(11)	$>f_{\omega }^{2}(2\uparrow \uparrow 12)>f_{\omega }^{2}(f_{3}(9))$	`1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RZ0LI_0LD1LE` (bbch)
BB(12)	$>f_{\omega }^{4}(2\uparrow \uparrow \uparrow 4-3)>f_{\omega }^{4}(f_{4}(2))$	`0LJ0RF_1LH1RC_0LD0LG_0RE1LD_1RF1RA_1RB1RF_1LC1LG_1LL1LI_1LK0LH_1RH1LJ_1RZ1LA_1RF1LL` (bbch)
BB(14)	$>f_{\omega +1}(65\,536)>g_{64}$	`1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RL0LI_0LL1LE_1LM1RZ_0LN1LF_0LJ---` (bbch)
BB(15)	$>f_{\omega +1}(f_{\omega }(10^{57}))$	`0RH1LD_1RI0RC_1RB1LD_0LD1LE_1LF1RA_1RG0LE_1RB1RG_1RD1RA_0LN0RJ_1RZ0LK_0LK1LL_1RG1LM_0LL0LL_1LO1LN_0LG1LN` (bbch)
BB(16)	$>f_{\omega +1}^{2}(10^{10^{57}})$
BB(18)	$>f_{\omega +2}(f_{\omega +1}^{3}(f_{\omega }^{2}(60)))$
BB(20)	$>f_{\omega +2}^{2}(21)$
BB(21)	$>f_{\omega ^{2}}^{2}(4\uparrow \uparrow 341)$
BB(40)	$>f_{\omega ^{\omega }}(75\,500)$
BB(41)	$>f_{\omega ^{\omega }}^{4}(32)$
BB(51)	$>f_{\varepsilon _{0}+1}(8)$

3 Symbols:


	Runtime	Champions
BB(1,3)	$1$	`1RZ------` (bbch)
BB(2,3)	$38$	`1RB2LB1RZ_2LA2RB1LB` (bbch)
BB(3,3)	$\geq 119\,112\,334\,170\,342\,541>10^{17}$	`0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC` (bbch)
BB(4,3)	$>2\uparrow \uparrow \uparrow (2^{2^{32}+1}-1)$	`0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD` (bbch)

4 Symbols:


	Runtime	Champions
BB(1,4)	$1$	`1RZ---------` (bbch)
BB(2,4)	$3\,932\,964$	`1RB2LA1RA1RA_1LB1LA3RB1RZ` (bbch)
BB(3,4)	$>(2\uparrow ^{15}5)+14$ ^[1]	`1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC` (bbch)

5 Symbols:


	Runtime	Champions
BB(1,5)	$1$	`1RZ------------` (bbch)
BB(2,5)	$>10^{10^{10^{3\,314\,360}}}$	`1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ` (bbch)
BB(3,5)	$>f_{\omega }(2\uparrow ^{15}5)>f_{\omega }^{2}(15)$	`1RB3LB4LC2RA4LB_2LC3RB1LC2RA1RZ_3RB1LB3LC2RC4LC` (bbch)

6 Symbols:


	Runtime	Champions
BB(1,6)	$1$	`1RZ---------------` (bbch)
BB(2,6)	$>10\uparrow \uparrow 10\uparrow \uparrow 10^{10^{115}}$ ^[2]	`1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA` (bbch)

Maximum Score Function (Σ(n,m))

2 Symbols:


	Score	Champions
Σ(1)	$1$	`1RZ---` (bbch)
Σ(2)	$4$	`1RB1LB_1LA1RZ` (bbch)
Σ(3)	$6$	`1RB1RZ_0RC1RB_1LC1LA` (bbch) `1RB1RC_1LC1RZ_1RA0LB` (bbch) `1RB1LC_1LA1RB_1LB1RZ` (bbch) `1RB1RA_1LC1RZ_1RA1LB` (bbch) `1RB1LC_1RC1RZ_1LA0LB` (bbch)
Σ(4)	$13$	`1RB1LB_1LA0LC_1RZ1LD_1RD0RA` (bbch) `1RB0RC_1LA1RA_1RZ1RD_1LD0LB` (bbch)
Σ(5)	$4098$	`1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA` (bbch) `1RB1RA_1LC1LB_1RA1LD_1RA1LE_1RZ0LC` (bbch)
Σ(6)	$>2\uparrow \uparrow 2\uparrow \uparrow 2\uparrow \uparrow 10$	`1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE` (bbch)
Σ(7)	$>2\uparrow ^{11}2\uparrow ^{11}3$	`1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF` (bbch)

3 Symbols:


	Score	Champions
Σ(1,3)	$1$	`1RZ------` (bbch)
Σ(2,3)	$9$	`1RB2LB1RZ_2LA2RB1LB` (bbch)
Σ(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 \geq 374\,676\,383}	`0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC` (bbch)
Σ(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}+1}-1}	`0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD` (bbch)

4 Symbols:


	Score	Champions
Σ(1,4)	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 1}	`1RZ---------` (bbch)
Σ(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 2050}	`1RB2LA1RA1RA_1LB1LA3RB1RZ` (bbch)
Σ(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 \geq (2 \uparrow^{15} 5) + 14 } ^[1]	`1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC` (bbch)

5 Symbols:


	Score	Champions
Σ(1,5)	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 1}	`1RZ------------` (bbch)
Σ(2,5)	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 > 10^{10^{10^{3\,314\,360}}}}	`1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ` (bbch)

6 Symbols:


	Score	Champions
Σ(1,6)	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 1}	`1RZ---------------` (bbch)
Σ(2,6)	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 10 \uparrow\uparrow 10^{10^{115}}} ^[2]	`1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA` (bbch)

Beeping Busy Beavers

Beeping Busy Beaver (BBB(n,m))

2 Symbols:


	Steps taken	Champions
BBB(1)	$1$
BBB(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_1LB1LA` (bbch)
BBB(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 55}	`1LB0RB_1RA0LC_1RC1RA` (bbch)
BBB(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 \geq 32\,779\,478}	`1RB1LD_1RC1RB_1LC1LA_0RC0RD` (bbch)
BBB(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 \geq 10^{14006}}	`1RB1LE_0LC0LB_0LD1LC_1RD1RA_0RC0LA` (bbch)

3 Symbols:


	Steps taken	Champions
BBB(1,3)
BBB(2,3)	$59$ ^[3]
BBB(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 \geq 10 \uparrow\uparrow 6}	`1RB0LB2LA_1LA0RC0LB_2RC2RB0LC` (bbch)

Note: The BBB(2,3) champion might be 1RB0LB2LA_1LA0RC0LB_2RC2RB0LC (bbch).

4 Symbols:


	Steps taken	Champions
BBB(1,4)
BBB(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 \geq 205\,770\,076\,433\,044\,242\,247\,859 > 2\times 10^{23}} ^[4]	`1RB2LA1RA1LB_0LB2RB3RB1LA` (bbch)

Beeping Booping Busy Beaver (BBBB(n,m))

There are currently no known/available Champions for this function.

Maximum Consecutive Ones Function (Num(n,m))

2 Symbols:


	Number of Ones	Champions
num(1)	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 1}	`1RZ---` (bbch)
num(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 4}	`1RB1LB_1LA1LZ` (bbch)
num(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 6}	`1RB1LC_1RC1LZ_1LA0LB` (bbch)
num(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 12}	`1RB0LA_1RC1LB_1LB1RD_1RZ0RA` (bbch)
num(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 165}	`1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB` (bbch) `0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC` (bbch)

Maximum Space Function (BB_space(n,m))

2 Symbols:


	Cells visited	Champions
BB_space(1,2)	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 2}
BB_space(2,2)	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 4}
BB_space(3,2)	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 7}
BB_space(4,2)	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 16}

Reversible Turing Machines

Maximum Shifts Function (BB_rev(n,m))

2 Symbols:


	Steps	Champions
BB_rev(1)
BB_rev(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}	`0RB1RZ_1LA1RB` (bbch)
BB_rev(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 17}	`0RB1RZ_0LC1RA_1RB1LC` (bbch)
BB_rev(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 48}	`1RB0LD_0LC0RB_1LA1LD_1LC1RZ` (bbch)
BB_rev(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 388}	`1RB0RD_1RC0RB_1RD1RZ_1LE1LA_0LE0LA` (bbch)
BB_rev(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 \geq 537\,556}	`1RB1LD_1LC1RE_0LD0LC_0RE0RF_0RA1RZ_1RF1RA` (bbch)
BB_rev(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^{19}}	`1RB1LD_0LC0LD_1LC1LA_0LA1RE_0RF0RE_0RG1RF_0RB1RZ` (bbch)

Maximum Score Function (Σ_rev(n,m))

2 Symbols:


	Score	Champions
Σ_rev(1)
Σ_rev(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 \geq 2}	`0RB1RZ_1LA1RB` (bbch)
Σ_rev(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 \geq 4}	`0RB1RZ_0LC1RA_1RB1LC` (bbch)
Σ_rev(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 \geq 6}	`1RB0LD_0LC0RB_1LA1LD_1LC1RZ` (bbch)
Σ_rev(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 \geq 16}	`1RB0RD_1RC0RB_1RD1RZ_1LE1LA_0LE0LA` (bbch)
Σ_rev(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 \geq 1161}	`1RB1LD_1LC1RE_0LD0LC_0RE0RF_0RA1RZ_1RF1RA` (bbch)

Blanking Busy Beaver (BLB(n,m))

2 Symbols:


	Steps	Champions
BLB(1)	inexistent	inexistent
BLB(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 \geq 8} ^[4]	`1RB0RA_1LB1LA` (bbch)
BLB(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 \geq 34} ^[5]	`1RB1LB_1LA1LC_1RC0LC` (bbch)
BLB(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 \geq 32\,779\,477}	`1RB1LD_1RC1RB_1LC1LA_0RC0RD` (bbch)

3 Symbols:


	Steps	Champions
BLB(1,3)	inexistent	inexistent
BLB(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 \geq 77} ^[5]	`1RB2LA_0RB1LA_0LB1RA` (bbch)

4 Symbols:


	Steps	Champions
BLB(1,4)	inexistent	inexistent
BLB(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 \geq 1\,367\,361\,263\,049} ^[5]	`1RB2RA1RA2RB_2LB3LA0RB0RA` (bbch)

Lazy Beaver

Shifts Function (LB(n,m))


	1 State	2 States	3 States	4 States	5 States	6 States
2 Symbols	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}	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 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 22}	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 72}	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 427}	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 8407}
3 Symbols	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}	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 23}	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 351}	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 189\,270}
4 Symbols	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}	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 93}	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 242\,789}
5 Symbols	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}	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 956}
6 Symbols	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}	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 33\,851}

Period-oriented Busy Beavers

Busy Preperiodic Beaver (BBS(n,m))

2 Symbols:


	Preperiod	Champions
BBS(1,2)
BBS(2,2)
BBS(3,2)	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 101}	`1RB1LB_0RC0LA_1LC0LA` (bbch)
BBS(4,2)	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 \geq 119\,120\,230\,102}	`1RB1LC_0LA1RD_0RB0LC_1LA0RD` (bbch)

3 Symbols: It seems that currently no information is available for this domain.

4 Symbols:


	Preperiod	Champions
BBS(1,4)
BBS(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 \geq 293\,225\,660\,896}	`1RB2LA0RA3LA_1LA1LB3RB1RA` (bbch)

Busy Periodic Beaver (BBP(n,m))

2 Symbols:


	Period	Champions
BBP(1,2)
BBP(2,2)
BBP(3,2)	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 92}	`1RB0LA_0RC1LA_1LC0RB` (bbch)
BBP(4,2)	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 \geq 212\,081\,736}	`1RB0LA_0RC1RD_1LD0RB_1LA1RB` (bbch)

3 Symbols: It seems that currently no information is available for this domain.

4 Symbols:


	Period	Champions
BBP(1,4)
BBP(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 \geq 33\,209\,131}	`1RB0RA3LB1RB_2LA0LB1RA2RB` (bbch)

Instruction-Limited Busy Beaver

Instruction-Limited Classical Busy Beaver Functions

Instruction-Limited Maximum Shifts Function (BBi(n))


	Steps	Champions
BBi(1)	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 1}	`0RH` (bbch) `1RH---` (bbch)
BBi(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 3}	`0RB---_1LA---` (bbch)
BBi(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 5}	`1RB1LB_1LA---` (bbch)
BBi(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 16}	`1RB---_0RC---_1LC0LA` (bbch)
BBi(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 37}	`1RB2LB---_2LA2RB1LB` (bbch)
BBi(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 123}	`1RB3LA1RA0LA_2LA------3RA` (bbch)
BBi(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 3\,932\,963}	`1RB2LA1RA1RA_1LB1LA3RB---` (bbch) `1RB2LA1RA_1LC1LA2RB_---1LA---` (bbch)
BBi(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 >6.889 \times 10^{1565}}	`1RB1LA------_1RC3LB1RB---_2LA2LC---0LC` (bbch)

Instruction-Limited Maximum Score Function (Σi(n))


	Score	Champions
Σi(1)	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 1}	`1RH---` (bbch)
Σi(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 2}	`1RB---_1LA---` (bbch)
Σi(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 4}	`1RB1LB_1LA---` (bbch)
Σi(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 5}	`1RB0LB---_1LA2RA---` (bbch)
Σi(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 9}	`1RB2LB---_2LA2RB1LB` (bbch)
Σi(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 14}	`1RB3LA1RA0LA_2LA------3RA` (bbch)
Σi(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 2050}	`1RB2LA1RA1RA_1LB1LA3RB---` (bbch) `1RB2LA1RA_1LC1LA2RB_---1LA---` (bbch)
Σi(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 >1.355 \times 10^{783}}	`1RB1LA------_1RC3LB1RB---_2LA2LC---0LC` (bbch)

Instruction-Limited Blanking Busy Beaver (BLBi(n))


	Steps	Champions
BLBi(1)	inexistent	inexistent
BLBi(2)	inexistent	inexistent
BLBi(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 4}
BLBi(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 12}
BLBi(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 30}
BLBi(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 77}
BLBi(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 808}
BLBi(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 \geq 1\,367\,361\,263\,049}	`1RB2RA1RA2RB_2LB3LA0RB0RA` (bbch)

Instruction-Limited Greedy Busy Beaver (gBBi(n))


	Steps	Champions
gBBi(1)	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 1}
gBBi(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 3}
gBBi(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 5}
gBBi(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 13}
gBBi(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 19}
gBBi(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 25}
gBBi(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 41}
gBBi(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 55}
gBBi(9)	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 238}
gBBi(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 941}
gBBi(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 1341}
gBBi(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 10465}
gBBi(13)	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 10675}
gBBi(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 \geq 9\,874\,580}	`0RB6RB1LB---3LA1RB7RB2LB_1LA2RB3LA4RB5RB1LB5LA---` (bbch)

Program-Limited Busy Beaver

Busy Beaver for Lambda Calculus

Regular Busy Beaver for Lambda Calculus (BBλ(n))

For n = 0,1,2,3,5 BBλ(n) is undefined, while for the rest of 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 20 \geq n } BBλ(n) = n.


	BBλ(n)	Champions
BBλ(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 22}	`\(\1 1) (1 (\2))`
BBλ(22)	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 24}	`\(\1 1) (1 (\\1))\(\1 1 1) (1 1)`
BBλ(23)	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 26}	`\(\1 1) (1 (\\2))`
BBλ(24)	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 30}	`\(\1 1 1) (1 (\1))`
BBλ(25)	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 42}	`\(\1 1) (\1 (2 1))`
BBλ(26)	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 52}	`(\1 1) (\\2 (1 2))`
BBλ(27)	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 44}	`\\(\1 1) (\1 (2 1))`
BBλ(28)	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 58}	`\(\1 1) (\1 (2 (\2))))`
BBλ(29)	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 223}	`\(\1 1) (\1 (1 (2 1)))`
BBλ(30)	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 160}	`(\1 1 1) (\\2 (1 2))` and `(\1 (1 1)) (\\2 (1 2))`
BBλ(31)	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 267}	`(\1 1) (\\2 (2 (1 2)))`
BBλ(32)	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 298 }	`\(\1 1) (\1 (1 (2 (\2))))`
BBλ(33)	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 1812}	`\(\1 1) (\1 (1 (1 (2 1))))`
BBλ(34)	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 327\,686}	`(\1 1 1 1) (\\2 (2 1))` and `(\1 (1 1) 1) (\\2 (2 1))`
BBλ(35)	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 5 \times 3^{3^{3}} +6 = 38\,127\,987\,424\,941 > 3.8 \times 10^{13}}	`(\1 1 1) (\\2 (2 (2 1)))`
BBλ(36)	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 5 \times 2^{2^{2^{3}}} +6 > 5.7 \times 10^{77}}	`(\1 1) (\1 (1 (\\2 (2 1))))`
BBλ(37)	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 BB \lambda(35) +2 =5 \times 3^{3^{3}} +8 = 38\,127\,987\,424\,943 > 3.8 \times 10^{13}}	`\(\1 1 1) (\\2 (2 (2 1)))`
BBλ(38)	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 \geq 5 \times 2^{2^{2^{2^{2}}}} +6 > 10^{19729}}	`(\1 1 1 1 1) (\\2 (2 1))` and `(\1 (1 1) 1 1) (\\2 (2 1))`
BBλ(39)	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 \geq 5 \times 3^{3^{3^{3}}} +6 > 10^{3\,638\,334\,640\,024}}	`(\1 1 1 1) (\\2 (2 (2 1)))`
BBλ(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 > (2 \uparrow\uparrow)^{15}33 > 10 \uparrow\uparrow\uparrow 16}	`(\1 1 1) (\1 (\\2 (2 1)) 1)`
BBλ(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 \geq 5 \times 3^{3^{85}} +6 > 10^{1.7 \times 10^{40}}}	`(\1 (\1 1) 1) (\\2 (2 (2 1)))`
BBλ(42)	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 \geq BB \lambda(40) + 2 > (2 \uparrow\uparrow)^{15}33 > 10 \uparrow\uparrow\uparrow 16}	`\(\1 1 1) (\1 (\\2 (2 1)) 1)`
BBλ(43)	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 \uparrow\uparrow\uparrow 2 \uparrow\uparrow 8}	`(\1 1) (\1 (\1 (\\2 (2 1)) 2))`
BBλ(44)	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\uparrow 10 \uparrow\uparrow\uparrow 16}	`(\1 1 1 1) (\1 (\\2 (2 1)) 1)`
BBλ(45)	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 \geq BB \lambda(43) + 2 > 2 \uparrow\uparrow\uparrow 2 \uparrow\uparrow\uparrow 2 \uparrow\uparrow 8}	`\(\1 1) (\1 (\1 (\\2 (2 1)) 2))`
BBλ(46)	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 \geq BB \lambda(44) + 2 > 10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 16}	`\(\1 1 1 1) (\1 (\\2 (2 1)) 1)`
BBλ(47)
BBλ(48)	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\uparrow 10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 16}	`(\1 1 1 1 1) (\1 (\\2 (2 1)) 1)`
BBλ(49)	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}(\frac{2 \uparrow\uparrow 6}{2}) > \text{Graham's Number}}	`(\1 1) (\1 (1 (\\1 2 (\\2 (2 1)))))`
BBλ(1850)	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 > \text{Loader's Number}}	`Too large for this list`

Oracle Busy Beaver for Lambda Calculus (BBλ₁(n))

Note that 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(n) = 6 + 5 \times BB \lambda(n)} .


	BBλ₁(n)	Champions
BBλ₁(1)	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 0}
BBλ₁(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 1}	`1`
BBλ₁(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 0}
BBλ₁(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 4}	`\1`
BBλ₁(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 5}	`\2`
BBλ₁(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 6}	`\\1`
BBλ₁(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 7}	`\\2`
BBλ₁(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 26}	`1 (\1)`
BBλ₁(9)	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 9}	`\\2`
BBλ₁(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 36}	`1 (\\1)`
BBλ₁(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 41}	`1 (\\2)`
BBλ₁(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 266}	`1 (1 (\1))`
BBλ₁(13)	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 51}	`1 (\\2)`
BBλ₁(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(36) = 25 \times 2^{2^{2^{3}}}+36 > 2.85 \times 10^{78}}	`1 (1 (\\1))`
BBλ₁(15)	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(41) \geq 25 \times 3^{3^{85}}+36 > 10^{1.7 \times 10^{40}}}	`1 (1 (\\2))`
BBλ₁(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(266)}	`1 (1 (1 (\1)))`
BBλ₁(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(51)}	`1 (1 (\\\2))`
BBλ₁(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^{4}(4) = f(f(266))}	`1 (\1) 1 (\1)`
BBλ₁(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^{3}(7) = f(f(41))}	`1 (1 (1 (\\2)))`
BBλ₁(20)	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^{6}(4) = f^{4}(266)}	`1 (\\1) 1 (\1)`
BBλ₁(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^{7}(4) = f^{5}(266)}	`1 (\\2) 1 (\1)`
BBλ₁(22)	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^{52}(4) = f^{50}(266)}	`1 (1(\1)) 1(\1)`
BBλ₁(28)	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 \geq f^{BB \lambda(f^{3}(4))}(4)}	`1 (\1) 1 (\1) 1 (\1)`
BBλ₁(29)	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 \geq f^{BB \lambda(f^{BB \lambda(f^{4}(4))+4}(4))+BB \lambda(f^{4}(4))+5}(4)}	`1(\1)(\1 2 1)(\1)`

Doodle Function (doodle(c,n))

doodle(1,n) = 1 and doodle(2,n) = n. Also note that doodle(c) = doodle(c,2).

2 Symbols:


	Runtime	Champions
doodle(3,2)	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 \geq 487}

Turmites

Terminating Turmites (TT(n,k), 1D Turmites)

Where n is the amount of states and k is the amount of symbols. There are currently no known/available Champions for this function.

2D Turmites (turNing machines)

There are currently no known/available Champions for this function.

References

↑ ^1.0 ^1.1 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.
↑ ^2.0 ^2.1 S. Ligocki, "BB(2,6) > 10↑↑10↑↑10↑↑3". Blog post, 2023. Accessed 15 August 2025.
↑ Nick Drozd. "BBB(3,3) > 10↑↑6". Accessed 15 August 2025.
↑ ^4.0 ^4.1 Nick Drozd. "Blanking Beavers". Accessed 15 August 2025.
↑ ^5.0 ^5.1 ^5.2 Nick Drozd. "Latest Beeping Busy Beaver Results". Accessed 15 August 2025.

[:0-1] 1.0 ^1.1 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.

[:1-2] 2.0 ^2.1 S. Ligocki, "BB(2,6) > 10↑↑10↑↑10↑↑3". Blog post, 2023. Accessed 15 August 2025.

[:2-3] Nick Drozd. "BBB(3,3) > 10↑↑6". Accessed 15 August 2025.

[:3-4] 4.0 ^4.1 Nick Drozd. "Blanking Beavers". Accessed 15 August 2025.

[:4-5] 5.0 ^5.1 ^5.2 Nick Drozd. "Latest Beeping Busy Beaver Results". Accessed 15 August 2025.

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@@ Line 328: / Line 328: @@
 |{{TM|1RB0LB2LA_1LA0RC0LB_2RC2RB0LC}}
 |}
+Note: The BBB(2,3) champion might be {{TM|1RB0LB2LA_1LA0RC0LB_2RC2RB0LC}}.
 '''4 Symbols:'''
 {| class="wikitable"

User:Polygon/Collection of BB Champions: Difference between revisions

Revision as of 10:48, 17 August 2025

Contents

State-and-Symbol-Limited Busy Beaver functions

Original Busy Beaver Functions

Maximum Shifts Function (S(n,m), also commonly called BB(n,m))

Maximum Score Function (Σ(n,m))

Beeping Busy Beavers

Beeping Busy Beaver (BBB(n,m))

Beeping Booping Busy Beaver (BBBB(n,m))

Maximum Consecutive Ones Function (Num(n,m))

Maximum Space Function (BB_space(n,m))

Reversible Turing Machines

Maximum Shifts Function (BB_rev(n,m))

Maximum Score Function (Σ_rev(n,m))

Blanking Busy Beaver (BLB(n,m))

Lazy Beaver

Shifts Function (LB(n,m))

Period-oriented Busy Beavers

Busy Preperiodic Beaver (BBS(n,m))

Busy Periodic Beaver (BBP(n,m))

Instruction-Limited Busy Beaver

Instruction-Limited Classical Busy Beaver Functions

Instruction-Limited Maximum Shifts Function (BBi(n))

Instruction-Limited Maximum Score Function (Σi(n))

Instruction-Limited Blanking Busy Beaver (BLBi(n))

Instruction-Limited Greedy Busy Beaver (gBBi(n))

Program-Limited Busy Beaver

Busy Beaver for Lambda Calculus

Regular Busy Beaver for Lambda Calculus (BBλ(n))

Oracle Busy Beaver for Lambda Calculus (BBλ₁(n))

Doodle Function (doodle(c,n))

Turmites

Terminating Turmites (TT(n,k), 1D Turmites)

2D Turmites (turNing machines)

References

Navigation menu

User:Polygon/Collection of BB Champions: Difference between revisions

Revision as of 10:48, 17 August 2025

State-and-Symbol-Limited Busy Beaver functions

Original Busy Beaver Functions

Maximum Shifts Function (S(n,m), also commonly called BB(n,m))

Maximum Score Function (Σ(n,m))

Beeping Busy Beavers

Beeping Busy Beaver (BBB(n,m))

Beeping Booping Busy Beaver (BBBB(n,m))

Maximum Consecutive Ones Function (Num(n,m))

Maximum Space Function (BBspace(n,m))

Reversible Turing Machines

Maximum Shifts Function (BBrev(n,m))

Maximum Score Function (Σrev(n,m))

Blanking Busy Beaver (BLB(n,m))

Lazy Beaver

Shifts Function (LB(n,m))

Period-oriented Busy Beavers

Busy Preperiodic Beaver (BBS(n,m))

Busy Periodic Beaver (BBP(n,m))

Instruction-Limited Busy Beaver

Instruction-Limited Classical Busy Beaver Functions

Instruction-Limited Maximum Shifts Function (BBi(n))

Instruction-Limited Maximum Score Function (Σi(n))

Instruction-Limited Blanking Busy Beaver (BLBi(n))

Instruction-Limited Greedy Busy Beaver (gBBi(n))

Program-Limited Busy Beaver

Busy Beaver for Lambda Calculus

Regular Busy Beaver for Lambda Calculus (BBλ(n))

Oracle Busy Beaver for Lambda Calculus (BBλ1(n))

Doodle Function (doodle(c,n))

Turmites

Terminating Turmites (TT(n,k), 1D Turmites)

2D Turmites (turNing machines)

References

Navigation menu

Maximum Space Function (BB_space(n,m))

Maximum Shifts Function (BB_rev(n,m))

Maximum Score Function (Σ_rev(n,m))

Oracle Busy Beaver for Lambda Calculus (BBλ₁(n))