Revision as of 17:08, 15 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).

Original Busy Beaver Functions

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

2 Symbols:


	Runtime	Champions
BB(1)	$1$	`1RZ---` (bbch)
BB(2)	$6$	`1RB1LB_1LA1RZ` (bbch) `1RB0LB_1LA1RZ` (bbch) `1RB1RZ_1LB1LA` (bbch) `1RB1RZ_0LB1LA` (bbch) `0RB1RZ_1LA1RB` (bbch)
BB(3)	$21$	`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)	$\geq 374\,676\,383$	`0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC` (bbch)
Σ(4,3)	$>2\uparrow \uparrow \uparrow 2^{2^{32}+1}-1$	`0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD` (bbch)

4 Symbols:


	Score	Champions
Σ(1,4)	$1$	`1RZ---------` (bbch)
Σ(2,4)	$2050$	`1RB2LA1RA1RA_1LB1LA3RB1RZ` (bbch)
Σ(3,4)	$\geq (2\uparrow ^{15}5)+14$ ^[1]	`1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC` (bbch)

5 Symbols:


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

6 Symbols:


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

Beeping Busy Beavers

Beeping Busy Beaver (BBB(n,m))

2 Symbols:


	Steps taken	Champions
BBB(1)	$1$
BBB(2)	$6$	`1RB1LB_1LB1LA` (bbch)
BBB(3)	$55$	`1LB0RB_1RA0LC_1RC1RA` (bbch)
BBB(4)	$\geq 32\,779\,478$	`1RB1LD_1RC1RB_1LC1LA_0RC0RD` (bbch)
BBB(5)	$\geq 10^{14006}$	`1RB1LE_0LC0LB_0LD1LC_1RD1RA_0RC0LA` (bbch)

3 Symbols:


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

4 Symbols:


	Steps taken	Champions
BBB(1,4)
BBB(2,4)	$\geq 205\,770\,076\,433\,044\,242\,247\,859>2\times 10^{23}$ ^[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)	$1$	`1RZ---` (bbch)
num(2)	$4$	`1RB1LB_1LA1LZ` (bbch)
num(3)	$6$	`1RB1LC_1RC1LZ_1LA0LB` (bbch)
num(4)	$12$	`1RB0LA_1RC1LB_1LB1RD_1RZ0RA` (bbch)
num(5)	$165$	`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)	$2$
BB_space(2,2)	$4$
BB_space(3,2)	$7$
BB_space(4,2)	$16$

Reversible Turing Machines

Maximum Shifts Function (BB_rev(n,m))

2 Symbols:


	Steps	Champions
BB_rev(1)
BB_rev(2)	$6$	`0RB1RZ_1LA1RB` (bbch)
BB_rev(3)	$17$	`0RB1RZ_0LC1RA_1RB1LC` (bbch)
BB_rev(4)	$48$	`1RB0LD_0LC0RB_1LA1LD_1LC1RZ` (bbch)
BB_rev(5)	$388$	`1RB0RD_1RC0RB_1RD1RZ_1LE1LA_0LE0LA` (bbch)
BB_rev(6)	$\geq 537\,556$	`1RB1LD_1LC1RE_0LD0LC_0RE0RF_0RA1RZ_1RF1RA` (bbch)
BB_rev(7)	$>10^{19}$	`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)	$\geq 2$	`0RB1RZ_1LA1RB` (bbch)
Σ_rev(3)	$\geq 4$	`0RB1RZ_0LC1RA_1RB1LC` (bbch)
Σ_rev(4)	$\geq 6$	`1RB0LD_0LC0RB_1LA1LD_1LC1RZ` (bbch)
Σ_rev(5)	$\geq 16$	`1RB0RD_1RC0RB_1RD1RZ_1LE1LA_0LE0LA` (bbch)
Σ_rev(6)	$\geq 1161$	`1RB1LD_1LC1RE_0LD0LC_0RE0RF_0RA1RZ_1RF1RA` (bbch)

Blanking Busy Beaver (BLB(n,m))

2 Symbols:


	Steps	Champions
BLB(1)
BLB(2)	$\geq 6$ ^[4]
BLB(3)	$\geq 34$ ^[4]
BLB(4)	$\geq 32\,779\,477$	`1RB1LD_1RC1RB_1LC1LA_0RC0RD` (bbch)

3 Symbols:


	Steps	Champions
BLB(1,3)
BLB(2,3)	$\geq 77$ ^[4]

4 Symbols:


	Steps	Champions
BLB(1,4)
BLB(2,4)	$\geq 1\,367\,361\,263\,049$ ^[4]

Lazy Beaver

Shifts Function (LB(n,m))


	1 State	2 States	3 States	4 States	5 States	6 States
2 Symbols	$2$	$7$	$22$	$72$	$427$	$8407$
3 Symbols	$2$	$23$	$351$	$189\,270$
4 Symbols	$2$	$93$	$242\,789$
5 Symbols	$2$	$956$
6 Symbols	$2$	$33\,851$

Period-oriented Busy Beavers

Busy Preperiodic Beaver (BBS(n,m))

2 Symbols:


	Preperiod	Champions
BBS(1,2)
BBS(2,2)
BBS(3,2)	$101$	`1RB1LB_0RC0LA_1LC0LA` (bbch)
BBS(4,2)	$\geq 119\,120\,230\,102$	`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)	$\geq 293\,225\,660\,896$	`1RB2LA0RA3LA_1LA1LB3RB1RA` (bbch)

Busy Periodic Beaver (BBP(n,m))

2 Symbols:


	Period	Champions
BBP(1,2)
BBP(2,2)
BBP(3,2)	$92$	`1RB0LA_0RC1LA_1LC0RB` (bbch)
BBP(4,2)	$\geq 212\,081\,736$	`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)	$\geq 33\,209\,131$	`1RB0RA3LB1RB_2LA0LB1RA2RB` (bbch)

Instruction-Limited Busy Beaver

Maximum amount of steps (BBi(n))


	Steps	Champions
BBi(1)	$1$	`0RH` (bbch) `1RH---` (bbch)
BBi(2)	$3$	`0RB---_1LA---` (bbch)
BBi(3)	$5$	`1RB1LB_1LA---` (bbch)
BBi(4)	$16$	`1RB---_0RC---_1LC0LA` (bbch)
BBi(5)	$37$	`1RB2LB---_2LA2RB1LB` (bbch)
BBi(6)	$123$	`1RB3LA1RA0LA_2LA------3RA` (bbch)
BBi(7)	$3\,932\,963$	`1RB2LA1RA1RA_1LB1LA3RB---` (bbch) `1RB2LA1RA_1LC1LA2RB_---1LA---` (bbch)
BBi(8)	$>6.889\times 10^{1565}$	`1RB1LA------_1RC3LB1RB---_2LA2LC---0LC` (bbch)

Maximum Score (Σi(n))


	Score	Champions
Σi(1)	$1$	`1RH---` (bbch)
Σi(2)	$2$	`1RB---_1LA---` (bbch)
Σi(3)	$4$	`1RB1LB_1LA---` (bbch)
Σi(4)	$5$	`1RB0LB---_1LA2RA---` (bbch)
Σi(5)	$9$	`1RB2LB---_2LA2RB1LB` (bbch)
Σi(6)	$14$	`1RB3LA1RA0LA_2LA------3RA` (bbch)
Σi(7)	$2050$	`1RB2LA1RA1RA_1LB1LA3RB---` (bbch) `1RB2LA1RA_1LC1LA2RB_---1LA---` (bbch)
Σi(8)	$>1.355\times 10^{783}$	`1RB1LA------_1RC3LB1RB---_2LA2LC---0LC` (bbch)

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 $20\geq n$ BBλ(n) = n.


	BBλ(n)	Champions
BBλ(21)	$22$	`\(\1 1) (1 (\2))`
BBλ(22)	$24$	`\(\1 1) (1 (\\1))\(\1 1 1) (1 1)`
BBλ(23)	$26$	`\(\1 1) (1 (\\2))`
BBλ(24)	$30$	`\(\1 1 1) (1 (\1))`
BBλ(25)	$42$	`\(\1 1) (\1 (2 1))`
BBλ(26)	$52$	`(\1 1) (\\2 (1 2))`
BBλ(27)	$44$	`\\(\1 1) (\1 (2 1))`
BBλ(28)	$58$	`\(\1 1) (\1 (2 (\2))))`
BBλ(29)	$223$	`\(\1 1) (\1 (1 (2 1)))`
BBλ(30)	$160$	`(\1 1 1) (\\2 (1 2))` and `(\1 (1 1)) (\\2 (1 2))`
BBλ(31)	$267$	`(\1 1) (\\2 (2 (1 2)))`
BBλ(32)	$298$	`\(\1 1) (\1 (1 (2 (\2))))`
BBλ(33)	$1812$	`\(\1 1) (\1 (1 (1 (2 1))))`
BBλ(34)	$327\,686$	`(\1 1 1 1) (\\2 (2 1))` and `(\1 (1 1) 1) (\\2 (2 1))`
BBλ(35)	$5\times 3^{3^{3}}+6>3.8\times 10^{13}$	`(\1 1 1) (\\2 (2 (2 1)))`
BBλ(36)	$5\times 2^{2^{2^{3}}}+6>5.7\times 10^{77}$	`(\1 1) (\1 (1 (\\2 (2 1))))`
BBλ(37)	$BB\lambda (35)+2=5\times 3^{3^{3}}+8>3.8\times 10^{13}$	`\(\1 1 1) (\\2 (2 (2 1)))`
BBλ(38)	$\geq 5\times 2^{2^{2^{2^{2}}}}+6>10^{10^{4}}$	`(\1 1 1 1 1) (\\2 (2 1))` and `(\1 (1 1) 1 1) (\\2 (2 1))`
BBλ(39)	$\geq 5\times 3^{3^{3^{3}}}+6>10^{10^{12}}$	`(\1 1 1 1) (\\2 (2 (2 1)))`
BBλ(40)	$>(2\uparrow \uparrow )^{15}33>10\uparrow \uparrow \uparrow 16$	`(\1 1 1) (\1 (\\2 (2 1)) 1)`
BBλ(41)	$\geq 5\times 3^{3^{85}}+6>10^{10^{40}}$	`(\1 (\1 1) 1) (\\2 (2 (2 1)))`
BBλ(42)	$\geq BB\lambda (40)+2>(2\uparrow \uparrow )^{15}33>10\uparrow \uparrow \uparrow 16$	`\(\1 1 1) (\1 (\\2 (2 1)) 1)`
BBλ(43)	$>2\uparrow \uparrow \uparrow 2\uparrow \uparrow \uparrow 2\uparrow \uparrow 8$	`(\1 1) (\1 (\1 (\\2 (2 1)) 2))`
BBλ(44)	$>10\uparrow \uparrow \uparrow 10\uparrow \uparrow \uparrow 16$	`(\1 1 1 1) (\1 (\\2 (2 1)) 1)`
BBλ(45)	$\geq BB\lambda (43)+2>2\uparrow \uparrow \uparrow 2\uparrow \uparrow \uparrow 2\uparrow \uparrow 8$	`\(\1 1) (\1 (\1 (\\2 (2 1)) 2))`
BBλ(46)	$\geq BB\lambda (44)+2>10\uparrow \uparrow \uparrow 10\uparrow \uparrow \uparrow 16$	`\(\1 1 1 1) (\1 (\\2 (2 1)) 1)`
BBλ(47)
BBλ(48)	$>10\uparrow \uparrow \uparrow 10\uparrow \uparrow \uparrow 10\uparrow \uparrow \uparrow 16$	`(\1 1 1 1 1) (\1 (\\2 (2 1)) 1)`
BBλ(49)	$>f_{\omega +1}({\frac {2\uparrow \uparrow 6}{2}})>{\text{Graham's Number}}$	`(\1 1) (\1 (1 (\\1 2 (\\2 (2 1)))))`
BBλ(1850)	$>{\text{Loader's Number}}$	`Too large for this list`

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

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


	BBλ₁(n)	Champions
BBλ₁(1)	$0$
BBλ₁(2)	$1$	`1`
BBλ₁(3)	$0$
BBλ₁(4)	$4$	`\1`
BBλ₁(5)	$5$	`\2`
BBλ₁(6)	$6$	`\\1`
BBλ₁(7)	$7$	`\\2`
BBλ₁(8)	$26$	`1 (\1)`
BBλ₁(9)	$9$	`\\2`
BBλ₁(10)	$36$	`1 (\\1)`
BBλ₁(11)	$41$	`1 (\\2)`
BBλ₁(12)	$266$	`1 (1 (\1))`
BBλ₁(13)	$51$	`1 (\\2)`
BBλ₁(14)	$f(36)=25\times 2^{2^{2^{3}}}+36>2.85\times 10^{78}$	`1 (1 (\\1))`
BBλ₁(15)	$f(41)\geq 25\times 3^{3^{85}}+36>10^{10^{40}}$	`1 (1 (\\2))`
BBλ₁(16)	$f(266)$	`1 (1 (1 (\1)))`
BBλ₁(17)	$f(51)$	`1 (1 (\\\2))`
BBλ₁(18)	$f^{4}(4)=f(f(266))$	`1 (\1) 1 (\1)`
BBλ₁(19)	$f^{3}(7)=f(f(41))$	`1 (1 (1 (\\2)))`
BBλ₁(20)	$f^{6}(4)=f^{4}(266)$	`1 (\\1) 1 (\1)`
BBλ₁(21)	$f^{7}(4)=f^{5}(266)$	`1 (\\2) 1 (\1)`
BBλ₁(22)	$f^{52}(4)=f^{50}(266)$	`1 (1(\1)) 1(\1)`
BBλ₁(28)	$\geq f^{BB\lambda (f^{3}(4))}(4)$	`1 (\1) 1 (\1) 1 (\1)`
BBλ₁(29)	$\geq f^{BB\lambda (f^{BB\lambda (f^{4}(4))+4}(4))+BB\lambda (f^{4}(4))+5}(4)$	`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)	$\geq 487$

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 ^4.2 ^4.3 ^4.4 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 ^4.2 ^4.3 ^4.4 Nick Drozd. "Latest Beeping Busy Beaver Results". Accessed 15 August 2025.

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@@ Line 339: / Line 339: @@
 |-
 |BBB(2,4)
-|<math>\geq 205\,770\,076\,433\,044\,242\,247\,859</math><ref name=":3" />
+|<math>\geq 205\,770\,076\,433\,044\,242\,247\,859 > 2\times 10^{23}</math><ref name=":3" />
 |{{TM|1RB2LA1RA1LB_0LB2RB3RB1LA}}
 |}

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

Revision as of 17:08, 15 August 2025

Contents

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

Maximum amount of steps (BBi(n))

Maximum Score (Σi(n))

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 17:08, 15 August 2025

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

Maximum amount of steps (BBi(n))

Maximum Score (Σi(n))

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))