Champions: Difference between revisions

Latest revision as of 10:48, 5 November 2026

Busy Beaver Champions are the current record holding Turing machines which 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. 1-state domains are omitted as BB(1,m) = 1 for m > 1.

Trivial Champions

BB(n,1) = n

BB(1,m) = 1

2-Symbol TMs

Rows are blank if no champion has been found which surpasses a smaller size problem. Also take note that the $f_{x} (n)$ used in the lower bounds represent the Fast-Growing Hierarchy while $↑$ represents Knuth's up-arrow notation; see measuring large numbers for more information. Machines below 6 states are listed in TNF format, where machines which tie for champion are all listed. Note that most champions above 6 states are self-reported and have not been independently verified.


Domain	Runtime	Champions	Discovered by	Verification
BB(2)	$6$	`1RB1LB_1LA1RZ` (bbch) `1RB0LB_1LA1RZ` (bbch) `1RB1RZ_1LB1LA` (bbch) `1RB1RZ_0LB1LA` (bbch) `0RB1RZ_1LA1RB` (bbch)	Tibor Radó	Direct Simulation
BB(3)	$21$	`1RB1RZ_1LB0RC_1LC1LA` (bbch)	Proven by Shen Lin	Direct Simulation
BB(4)	$107$	`1RB1LB_1LA0LC_1RZ1LD_1RD0RA` (bbch)	Allen Brady	Direct Simulation
BB(5)	$47 176 870$	`1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA` (bbch)	Heiner Marxen & Jürgen Buntrock in 1989	Direct Simulation
BB(6)	$> 10 ↑ ↑ 10 ↑ ↑ 10 ↑ ↑ 8$	`1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE` (bbch)	mxdys in 2025	See mxdys's analysis on the TM page
BB(7)	$> 3 ↑^{20} 3 > f_{ω} (20)$	`1RB0RG_1RC1RB_0RD1RZ_0LE0LD_0LF1LE_1RA1LF_1LC0RB` (bbch)	Jeff Ketchersid and Gemini in 10/2026 (claimed)	Claimed analysis by Claude never verified.
BB(8)	$> f_{ω}^{3} (12)$	`1RB0RA_1LC1LF_1RD0LB_1RA1LE_1LH0LC_1RG1LD_0RG0RF_1RG1RZ` (bbch)	Jeff Ketchersid and Gemini in 10/2026 (claimed)	Claimed analysis by Claude never verified.
BB(9)	$> f_{ω}^{7} (12)$	`1RB0RA_1LC1LF_1RD0LB_1RA1LE_0LH0LC_1RG1LD_0RG0RF_0LI1RZ_1RI1RC` (bbch)	Jeff Ketchersid and Gemini in 10/2026 (claimed)	Claimed analysis by Claude never verified.
BB(10)	$> f_{ω + 1} (2 ↑^{36} 3) > g_{64}$	`1RB0RA_1LC1LF_1RD0LB_1RA1LE_1LI0LC_0RG1LD_1RH1LG_1LC0RG_0LJ0LI_1RZ0LC` (bbch)	Jeff Ketchersid and Claude in 10/2026 (claimed)	Claimed analysis by Claude never verified.
BB(11)	$> f_{ω + 1} (f_{ω}^{2} (5))$	`1RG0LH_1RK1RC_0LD1LA_0RE1LD_0LI1RF_1RZ0RG_1RB1RG_1LA1LH_0LK0LJ_1LH1LI_1LJ1RE` (bbch)	Jeff Ketchersid and Gemini in 10/2026 (claimed)	Claimed analysis by Claude never verified.
BB(12)	$> f_{ω + 2} (f_{ω + 1}^{2} (3))$	`1RB1RA_1RI1RC_0LD1LG_0RE1LD_1LK1RF_1RG0RA_1RA0LH_1LG1LH_1RE0LJ_1LH1LI_1RZ0LL_0LH1LK` (bbch)	Jeff Ketchersid and Gemini in 10/2026 (claimed)	Claimed analysis by Claude never verified.
BB(13)	$> f_{ω + 2}^{6} (f_{ω + 1}^{2} (3))$	`1RB1RA_1RI1RC_0LD1LG_0RE1LD_1LK1RF_1RM0RA_1RA0LH_1LG1LH_1RE0LJ_1LH1LI_0LL0LL_0LH1LK_1RZ0LH` (bbch)	Jeff Ketchersid, Claude and Gemini in 10/2026 (claimed)	Claimed analysis by Claude never verified.
BB(14)	$> f_{ω + 3} (17)$	`1RB1RA_1RI1RC_0LD1LG_0RE1LD_1LK1RF_1RM0RA_1RA0LH_1LG1LH_1RE0LJ_1LH1LI_0LL0LL_0LN1LK_1RZ0LH_0LG1LJ` (bbch)	Jeff Ketchersid, Claude and Gemini in 11/2026 (claimed)	Claimed analysis by Claude never verified.
BB(15)
BB(16)
BB(17)	$> f_{ω + 3}^{3} (9)$	`1LB1LA_1RC0LA_1RD1RC_1RE1RK_1RF0LJ_1LG1RI_1RM0LM_1LG0RC_0RN0LE_1LA1LE_0LL1LB_0RM1LL_1LF1RH_1RQ0LO_1LP1LN_0RB1LI_1RZ1LO` (bbch)	Jeff Ketchersid, Claude and Gemini in 11/2026 (claimed)	Claimed analysis by Claude never verified.
BB(18)	$> f_{ω + 4} (228)$	`1LB1LA_1RC0LA_1RD1RC_1RE1RK_1RF0LJ_1LG1RI_1RM0LM_1LG0RC_0RN0LE_1LA1LE_0LL1LB_0RM1LL_1LF1RH_1RQ0LO_1LP1LR_0RB1LI_1RZ1RR_1RN0LO` (bbch)	Jeff Ketchersid, Claude and Gemini in 11/2026 (claimed)	Claimed analysis by Claude never verified.
BB(19)	$> f_{ω + 7}^{2} (5)$	`1RQ1RL_0LI1RC_0LD1LF_0RA1LD_1RB1RE_1LH0LG_1LF1LG_1RE1RM_1LJ1LI_0LK1LI_1RL1RA_0RL0RE_0LN1RM_1LO0LO_1RE1LP_1LN1LN_1LR1RQ_1RZ1LS_0LE0LR` (bbch)	Jacobzheng in 2026	Not independently verified.
BB(20)	$> f_{ω \times 2} (f_{ω + 2}^{2} (f_{10} (2)))$	`1LH0LG_0LI1RC_0LD1LA_0RE1LD_1RQ1RL_1RB1RF_1LA1LG_1RF1RM_1LJ1LI_0LK1LI_1RL1RE_0RL0RF_0LN1RM_0RF0LO_0RF1LP_0RF1LN_1LR1RQ_1RZ1LS_0LF1LT_0LF0LR` (bbch)	Jacobzheng in 2026	Not independently verified.
BB(21)	$> f_{ω^{2}}^{2} (4 ↑ ↑ 341)$	`0LI0LF_0RJ1RG_0RD1LC_1RH1RE_1LO0RH_1LA1LF_0LC1LA_1RB1RH_1RD0LF_1LP0RK_0LM1LL_0LL1LM_1LE1LN_0RQ0LM_0RP1LO_1LR0RH_1LF1RQ_1RZ0LS_1LH0LT_1LH1LU_0LE1LR` (bbch)	Racheline in 2024	Not independently verified.
...
BB(29)	$> f_{ω^{ω}} (3)$	[1]	mxdys in 10/2026 (claimed)	Claimed analysis by Claude never verified.
BB(31)	$> f_{ω ↑ ↑ 4} (3)$	[2]	mxdys in 10/2026 (claimed)	Claimed analysis by Claude never verified.
BB(33)	$> f_{ω ↑ ↑ 6} (3)$	[3]	mxdys in 10/2026 (claimed)	Claimed analysis by Claude never verified.
BB(48)	$> f_{ε_{1}} (3)$	[4]	roromachine14 and Gemini in 2026	Not independently verified.
BB(150)	$> f_{l i m (B M S)} (10 ↑ ↑ 15)$	too large to show	Patcail in 2025^[1]	Not independently verified.
BB(1015)	$> D^{5} (99)$ = Loader's Number		CatsAreFluffy in 2024^[2]	Not independently verified.

Conjectured


Domain	Runtime	Champions	Discovered by	Notes
BB(67)	$> q^{81} (q (5) - 2)$	[5]	racheline in 2025	$q (n)$ is derived from Laver tables. From racheline: "The known information about q(n) isn't enough to prove that this machine scores higher than the shown champions with fewer states, or that it scores lower than the shown champions with more states." If q(5) doesn't exist (this can only happen if ZFC+I3 is inconsistent), then this machine doesn't halt.

3-Symbol TMs


Domain	Runtime	Champions	Discovered by	Verification
BB(2,3)	$38$	`1RB2LB1RZ_2LA2RB1LB` (bbch)	Allen Brady in 1988	Direct Simulation
BB(3,3)	$> 1 0^{17}$	`0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC` (bbch)	Terry & Shawn Ligocki in 2007	Analysis by Pascal Michel
BB(4,3)	$> 10 ↑^{4} 4$	`1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD` (bbch)	Pavel Kropitz in 2024	See Polygon's analysis on the TM page
BB(5,3)
BB(6,3)	$> f_{ω}^{2} (10 ↑ ↑ ↑ 6)$	`1LE2LD2LC_2RB1RB1RA_2RB1LC0LC_1RB1LD2LD_2RD2LE2LF_1RZ---1LE` (bbch)	Jacobzheng in 2026	Not independently verified.
BB(7,3)
BB(8,3)	$> f_{ω + 1} (f_{ω}^{4} (f_{7} (2))) > g_{64}$	`1RD2RE2LA_2RC2LC2RB_1LH2RF1LA_2RC1RD2RB_---1LC2RE_1RZ0LF1LG_1RD2LG2LG_0LA0LD1LH` (bbch)	Jacobzheng in 2026	Not independently verified.
BB(9,3)
BB(10,3)
BB(11,3)	$> f_{ω + 3}^{2} (4)$	`1LD2RG2LA_2LE2LH2RB_2LE1RC2RB_0RC1RD0LG_0LF1LE1LE_1RG1RI---_0RC1LH2RG_1RC2LH1LA_1RI1RI1LJ_0LA2LK---_1RZ2LJ---` (bbch)	Jacobzheng in 2026	Not independently verified.
...
BB(36,3)	$> f_{ε_{0}} (7)$		Wythagoras in 2014^[3]	Not independently verified.
BB(37,3)	$> f_{ε_{0}} (373 676 378)$		Wythagoras in 2014^[4]	Not independently verified.

4-Symbol TMs


Domain	Runtime	Champions	Discovered by	Verification
BB(2,4)	$3 932 964$	`1RB2LA1RA1RA_1LB1LA3RB1RZ` (bbch)	Terry & Shawn Ligocki in 2005	Pascal Michel, Heiner Marxen, Allen Brady
BB(3,4)	$> 2 ↑^{15} 5$	`1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC` (bbch)	Pavel Kropitz in 2024	Analysis by Shawn Ligocki
BB(4,4)	$> 2 ↑^{509} 3 > f_{ω} (508)$	`0LB3LB1RZ2RA_1LD3RB1LC2RA_3RB1LB3LC2RC_0RD2RC2LB0RA` (bbch)	User:Loader3229 in 2026	Claimed analysis by MiniMax Not independently verified.
BB(5,4)	$> f_{ω}^{2} (10 ↑^{4} 10 ↑ ↑ 65 533)$	`1LD2RA3RB1LC_1LD2LA3RB---_2RA1LA3RC2LC_2RA---2LD2LE_------1RZ1LD` (bbch)	Jacobzheng in 2026	Not independently verified.
BB(6,4)	$> f_{ω + 1} (10 ↑ ↑ 65 533) > g_{64}$	`1LF2RA3RB---_3RD2LB3RB1LC_2RA1LB3RC2LC_1LD2RE0LA1LD_1RZ0LE1LF---_2RA---2LF2LF` (bbch)	Jacobzheng in 2026	Not independently verified.
BB(7,4)
BB(8,4)	$> f_{ω + 2} (f_{ω}^{4} (12))$	`1RC3LB2RD2RA_1RF3RB1LC2RA_3RB1LB3LC2RC_0RF2LD1LD2LE_3RE3LB2RE2LE_0LG0LH1RZ3RB_1LG2RD1LG3RG_0LH0LC0LH3RD` (bbch)	User:Loader3229 in 2026	Not independently verified.
BB(9,4)	$> f_{ω + 3} (16)$	`2LI3LB2RD2RA_2LC3RB1LC2RA_3RB1LB3LC2RC_0RF2LD1LD2LE_3RE3LB2RE2LE_0LG0LH1RZ---_1LG2RD1LG3RG_0LH---0LH3RD_2LB---1LI3RF` (bbch)	User:Loader3229 in 2026	Not independently verified.
BB(10,4)
BB(11,4)	$> f_{ω \times 2} (2 ↑^{11} 6)$	`1RK3LB1RZ2RA_0LG1LE1LD2RA_3RB1LB3LC2RC_3RE0LI3LC2RC_1RJ3RE3LH2LF_3RF2RF2LE1LF_3LC3LH2LJ2RG_0LE3RH1LI2RG_3RH1LH3LI2RI_0LB0LJ3LJ3RK_2LC0LD2RA3RK` (bbch)	User:Loader3229 in 2026	Not independently verified.
...
BB(31,4)	$> f_{ε_{0}} (373 676 378)$		Wythagoras in 2014^[5]	Not independently verified.

5-Symbol TMs

Domain	Runtime	Champions	Discovered by	Verification
BB(2,5)	$> 1 0^{1 0^{1 0^{3 314 360}}}$	`1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ` (bbch)	Daniel Yuan in 2024	mxdys in Rocq
BB(3,5)	$> f_{ω} (2 ↑^{15} 5) > f_{ω}^{2} (15)$	`1RB3LB4LC2RA4LB_2LC3RB1LC2RA1RZ_3RB1LB3LC2RC4LC` (bbch)	Racheline in 2024	Not independently verified.
BB(4,5)	$> f_{ω + 1} (27 041) > g_{64}$	`1RB3LB4LC2RA4LB_2LC3RB1LC2RA4RD_3RB1LB3LC2RC4LC_2RC2RD1RZ4RB1LC` (bbch)	User:Loader3229 in 2026	Not independently verified.
BB(5,5)	$> f_{ω + 1} (f_{ω}^{4} (6))$	`1LB3LB4LC2RA4LB_3LE3RB1LC2RA4RD_3RB1LB3LC2RC4LC_1RZ------4LD4LE_3RB------4LE3LC` (bbch)	User:Loader3229 in 2026	Not independently verified.
BB(6,5)	$> f_{ω + 3} (11)$	`2LE3LB4LC2RA4LB_4RA3RB1LC2RA4RD_3RB1LB3LC2RC4LC_1RZ3LF1LA4LD4LE_3RB---0RD4LE3LC_4LC------3LF3LF` (bbch)	User:Loader3229 in 2026	Not independently verified.
BB(7,5)	$> f_{ω + 3}^{2} (10)$	`2LE3LB4LC2RA4LB_4RA3RB1LC2RA4RD_3RB1LB3LC2RC4LC_1RZ3LF1LG4LD4LE_3RB---1LE4LE3LC_4LC------3LF3LF_3LF------1LG1LG` (bbch)	User:Loader3229 in 2026	Not independently verified.
BB(8,5)	$> f_{ω \times 2 + 1} (93)$	`2RG3LB4LC2RA4LB_1RZ---1LD2RA4LD_3RB1LB3LC2RC4LC_3RE---3LC2RC3LC_---3RE4LE4LH4RB_4LE3LG3LB2RF4LG_2LH3RG1LH2RF2RA_3RG1LG3LH2RH4LH` (bbch)	User:Loader3229 in 2026	Not independently verified.
...
BB(19,5)	$> f_{ε_{0}} (1.7 \cdot 1 0^{352})$	`1RB2LA1RA2LB2LA_0LA2RB3RB4RA1LQ_1RZ1RC2LD------_0LK3RD2RD2RD4RD_------0RH1LS0RF_1LG1RF2RF---4RF_4LE1LG2LG---4LG_0LI1RH2RH---4RH_0RK0LJ------4RK_2LE1LJ2LJ---4LJ_4RP---0LE---0LK_2RQ---2LL---4LL_2LN---2RM3RM4RM_4RQ2RQ2LN3LN4LN_4LN---2RO3RO4RO_3LL1LP2LP1LQ4LP_1RC3RR1RM3LP0RO_3LL1RR2RR0RR4RR_1RC1LS2LS1LS4LS` (bbch)	Wythagoras in 2014^[6]	Not independently verified.
BB(94,5)	$> f_{ψ_{0} (Ω_{2})} (1.7 \cdot 1 0^{352})$		Wythagoras in 2014^[7]	Not independently verified.

6-Symbol TMs

Domain	Runtime	Champions	Discovered by	Verification
BB(2,6)	$> 10 ↑ ↑ 10 ↑ ↑ 1 0^{1 0^{115}}$	`1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA` (bbch)	Pavel Kropitz in 2023	Analysis by Shawn Ligocki
BB(3,6)	$> f_{ω}^{3} (15)$	`1RB3LB4LC2RA4LB5LB_2LC3RB1LC2RA5LC1RZ_3RB1LB3LC2RC4LC5LC` (bbch)	User:Loader3229 in 2026	Not independently verified.
BB(4,6)	$> f_{ω + 2} (29)$	`5LD3LB5LC2RA4LB4LC_1RZ3RB1LC2RA3RD0LA_3RB1LB3LC2RC4LC1RA_3RB0LA2LC4LD4LC4LD` (bbch)	User:Loader3229 in 2026	Not independently verified.
BB(5,6)	$> f_{ω + 3} (31)$	`1LE3LB2LA2RA4LB5RA_1RZ3RB1LC2RA3RD4RA_3RB1LB3LC2RC4LC2LB_3RB0LA5LE4LD4LC4LD_4LC5LC0RE5LE1RE2RE` (bbch)	User:Loader3229 in 2026	Not independently verified.
BB(6,6)	$> f_{ω \times 2} (89)$	`4LF3LB1RZ2RA4LB---_2LC3RB1LD2RA3LF---_3RB1LB3LC2RC4LC0LE_3RB---3LC2RC---3RE_5RC3RE---4LC------_5RB0LF1RB1LF---5RB` (bbch)	User:Loader3229 in 2026	Not independently verified.
BB(7,6)	$> f_{ω^{2}} (63)$	`2LE3LB1RZ2RA4LB2LD_0LA3RB1LD2RA3LF5RB_3RB1LB3LC2RC4LC1LE_3RB3RE3LC2RC---3RD_5RB3RE0LG4LC3LG5LE_5RB5RB---1LF---5LF_5LF---3RC1LG---5LG` (bbch)	User:Loader3229 in 2026	Not independently verified.
BB(8,6)	$> f_{ω^{2} + 1} (7)$	`0LC3LB2LH2RA4LB1RZ_3LH3RB1LD2RA3LF5RB_3RB1LB3LC2RC4LC1LE_3RB3RE3LC2RC2LD3RD_5RB3RE---4LC3LG5LE_5RB5RB---1LF5LF5LF_5LF4RG1LB1LG5LD5LG_3LE---1LH1LH---5RG` (bbch)	User:Loader3229 in 2026	Not independently verified.
...
BB(61,6)	$> f_{ψ_{0} (Ω_{2})} (1.7 \cdot 1 0^{352})$		Wythagoras in 2014^[8]	Not independently verified.

7-Symbol TMs

Domain	Runtime	Champions	Discovered by	Verification
BB(2,7)	$> 10 ↑ ↑ 10 ↑ ↑ 10 ↑ ↑ 155$	`1RB3RB4LA1LB5LA6LB5RA_2LA6RA4RB1RZ3LB6LA4RB` (bbch)	roromachine14 in 2026	Not independently verified.
BB(3,7)	$> f_{ω + 1} (117) > g_{64}$	`6LC3LB6RA2RA4LB5LC5LA_1RZ3RB1LC2RA3RB4LC5RA_3RB1LB3LC2RC4LC1RA6LA` (bbch)	User:Loader3229 in 2026	Not independently verified.
BB(4,7)	$> f_{ω + 3} (28)$	`5LC3LB0RD2RA4LB6LB1LC_1RZ3RB1LC2RA3RD2LC4LC_3RB1LB3LC2RC4LC1LA5LD_3RB6LA6LC4LD4LC4LD6LC` (bbch)	User:Loader3229 in 2026	Not independently verified.
...
BB(18,7)	$> f_{ε_{0}} (1.7 \cdot 1 0^{352})$	`1RB2LA1RA2LB2LA------_0LA2RB3RB4RA1LP------_0RZ1RC2LD------------_0LJ3RD2RD2RD4RD------_4LE1LE0RG1LR0RF2LE4LE_1LE1RF5RF---6RF------_0LH1RG2RG---4RG------_0RJ0LI------4RJ------_2LE1LI2LI---4LI------_4RO---0LE---0LJ------_2RP---2LK---4LK------_2LM---2RL3RL4RL------_4RP2RP2LM3LM4LM------_4LM---2RN3RN4RN------_3LK1LO2LO1LP4LO------_1RC3RQ1RL3LO0RN------_3LK1RQ2RQ0RQ4RQ------_1RC1LR2LR1LR4LR------` (bbch)	Wythagoras in 2014^[9]	Not independently verified.
BB(46,7)	$> f_{ψ_{0} (Ω_{2})} (1.7 \cdot 1 0^{352})$		Wythagoras in 2014^[10]	Not independently verified.
BB(134,7)	$> f_{ψ_{0} (Ω_{ω})} (2 050)$		LittlePeng9+Wythagoras in 2014^[11]	Not independently verified.

8-Symbol TMs

Domain	Runtime	Champions	Discovered by	Verification
BB(2,8)	$> 10 ↑ ↑ 10 ↑ ↑ 10 ↑ ↑ 10 ↑ ↑ 155$	`1RB3RB4LA1LB5LA6LB5RA1RZ_2LA6RA4RB7RA3LB6LA4RB4RA` (bbch)	roromachine14 in 2026	Not independently verified.
...
BB(17,8)	$> f_{ε_{0}} (1.7 \cdot 1 0^{352})$	`1RB2LA1RA2LB2LA---------_0LA2RB3RB4RA1LO---------_0RZ1RC2LD---------------_0LJ3RD2RD2RD4RD---------_4LE1LE0RG1LQ0RF2LE4LE---_1LE1RF5RF---6RF---------_0LH1RG2RG---4RG---------_0RJ0LI------4RJ---------_2LE1LI2LI---4LI---------_4RN---0LE---0LJ---------_2RO2RO2LK3LK4LK2LK4LK4RO_2LK---5RL3RL6RL---------_4LK---5RM3RM6RM---------_3LK1LN2LN1LO4LN---------_1RC3RP1RL3LN7RM---------_3LK1RP2RP0RP4RP---------_1RC1LQ2LQ1LQ4LQ---------` (bbch)	Wythagoras in 2014^[12]	Not independently verified.

9-Symbol TMs

Domain	Runtime	Champions	Discovered by	Verification
BB(2,9)	$> 10 ↑ ↑ 10 ↑ ↑ 10 ↑ ↑ 10 ↑ ↑ 10 ↑ ↑ 155$	`1RB3RB4LA1LB5LA6LB5RA8RA1RZ_2LA6RA4RB7RA3LB6LA4RB4RA4RA` (bbch)	roromachine14 in 2026	Not independently verified.
...
BB(42,9)	$> f_{ψ_{0} (Ω_{2})} (1.7 \cdot 1 0^{352})$		Wythagoras in 2014^[13]	Not independently verified.

Zoology

There are many types of champions.

Note: the scale here is not formally defined. It mostly serves to estimate the average values produced by a type of champions.


Classification	Description	Examples	Scale
Trivial	The simplest champions that can exist. They mostly appear in some BB-adjacent functions like BBf or BBCS.	`1RZ---` (bbch) `0RA_0RZ` (bbch) `0RA_0RB_0RZ` (bbch)	$O (n)$
Chaotic	Have a chaotic behavior with repeating patterns that go back and forth.	`1RB1LB_1LA1RZ` (bbch) `1RB1RZ_1LB0RC_1LC1LA` (bbch) `1RB1LB_1LA0LC_1RZ1LD_1RD0RA` (bbch)	$O (2^{n})$
Countdown	Compute a number then "count down" (usually while bouncing) until reaching 0. They are common in some BB-adjacent functions like BBf.	`1RB2LB1RZ_2LA2RB1LB` (bbch)	$O (n^{2})$
Collatz-like	Compute a Collatz-like function. Repeatedly multiply and add a number depending of its modulo until reaching a number with a certain modulo.	`1RB2LA1RA1RA_1LB1LA3RB1RZ` (bbch) `1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA` (bbch)	$O (2^{n})$
Random walk	Compute a Collatz-like function with a random walk.		$O (2^{2^{n}})$
Tetrational			$O (2 ↑ ↑ n)$
Ackermannian			$O (2 ↑^{n} 3)$

References

[1] ttps://discord.com/channels/960643023006490684/1026577255754903572/1328863966688182345

[2] ttps://github.com/CatsAreFluffy/metamath-turing-machines/commit/85948b04fc4aeb983ca6d63d6aee5ad6ef308bfe

[3] ttps://googology.fandom.com/wiki/User:Wythagoras/Rado%27s_sigma_function/BB(36,3)

[4] ttps://googology.fandom.com/wiki/User:Wythagoras/Rado%27s_sigma_function/BB(37,3)

[5] ttps://googology.fandom.com/wiki/User:Wythagoras/Rado%27s_sigma_function/BB(31,4)

[6] ttps://googology.fandom.com/wiki/User:Wythagoras/Rado%27s_sigma_function/BB(19,5)

[7] ttps://googology.fandom.com/wiki/User_blog:Wythagoras/Hydra_machines

[8] ttps://googology.fandom.com/wiki/User_blog:Wythagoras/Hydra_machines

[9] ttps://googology.fandom.com/wiki/User:Wythagoras/Rado%27s_sigma_function/BB(18,7)

[10] ttps://googology.fandom.com/wiki/User_blog:Wythagoras/Hydra_machines

[11] ttps://googology.fandom.com/wiki/User:Wythagoras/Rado%27s_sigma_function/Analysis_of_LittlePeng9%27s_work/Hydra_machines

[12] ttps://googology.fandom.com/wiki/User:Wythagoras/Rado%27s_sigma_function/BB(17,8)

[13] ttps://googology.fandom.com/wiki/User_blog:Wythagoras/Hydra_machines

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[8]

[9]

[10]

[11]

[12]

[13]

Champions: Difference between revisions

Latest revision as of 10:48, 5 November 2026

Contents

Trivial Champions

2-Symbol TMs

Conjectured

3-Symbol TMs

4-Symbol TMs

5-Symbol TMs

6-Symbol TMs

7-Symbol TMs

8-Symbol TMs

9-Symbol TMs

Zoology

References

Navigation menu

@@ Line 52: / Line 52: @@
 |<math>> 3 \uparrow^{20} 3 > f_\omega(20)</math>
 |{{TM|1RB0RG_1RC1RB_0RD1RZ_0LE0LD_0LF1LE_1RA1LF_1LC0RB|halt}}
-|Jeff Ketchersid and Gemini in 2026 (claimed)
+|Jeff Ketchersid and Gemini in 10/2026 (claimed)
 |[https://github.com/jeff87654/busy-beaver/blob/main/BB7/1RB0RG_1RC1RB_0RD---_0LE0LD_0LF1LE_1RA1LF_0LD0RB.md Claimed analysis by Claude] never verified.
 |-
@@ Line 58: / Line 58: @@
 |<math>> f_\omega^3(12)</math>
 |{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1LH0LC_1RG1LD_0RG0RF_1RG1RZ|halt}}
-|Jeff Ketchersid and Gemini in 2026 (claimed)
+|Jeff Ketchersid and Gemini in 10/2026 (claimed)
 |[https://github.com/jeff87654/busy-beaver/blob/main/BB8/1RB0RA_1LC1LF_1RD0LB_1RA1LE_1LH0LC_1RG1LD_0RG0RF_1RG---.md Claimed analysis by Claude] never verified.
 |-
@@ Line 64: / Line 64: @@
 |<math>> f_\omega^7(12)</math>
 |{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_0LH0LC_1RG1LD_0RG0RF_0LI1RZ_1RI1RC|halt}}
-|Jeff Ketchersid and Gemini in 2026 (claimed)
+|Jeff Ketchersid and Gemini in 10/2026 (claimed)
 |[https://github.com/jeff87654/busy-beaver/blob/main/BB9/1RB0RA_1LC1LF_1RD0LB_1RA1LE_0LH0LC_1RG1LD_0RG0RF_0LI---_1RI1RC.md Claimed analysis by Claude] never verified.
 |-
@@ Line 70: / Line 70: @@
 |<math>> f_{\omega+1}(2 \uparrow^{36} 3) > g_{64}</math>
 |<span style="word-break:break-all">{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1LI0LC_0RG1LD_1RH1LG_1LC0RG_0LJ0LI_1RZ0LC|halt}}</span>
-|[https://discord.com/channels/960643023006490684/1331570843829932063/1557806386073702622 Jeff Ketchersid and Claude in 2026 (clamied)]
+|[https://discord.com/channels/960643023006490684/1331570843829932063/1557806386073702622 Jeff Ketchersid and Claude in 10/2026 (claimed)]
 |[https://github.com/jeff87654/busy-beaver/tree/main/BB10 Claimed analysis by Claude] never verified.
 |-
@@ Line 76: / Line 76: @@
 |<math>> f_{\omega+1}(f_\omega^2(5))</math>
 |<span style="word-break:break-all">{{TM|1RG0LH_1RK1RC_0LD1LA_0RE1LD_0LI1RF_1RZ0RG_1RB1RG_1LA1LH_0LK0LJ_1LH1LI_1LJ1RE|halt}}</span>
-|Jeff Ketchersid and Gemini in 2026 (claimed)
+|Jeff Ketchersid and Gemini in 10/2026 (claimed)
 |[https://github.com/jeff87654/busy-beaver/tree/main/BB11 Claimed analysis by Claude] never verified.
 |-
@@ Line 82: / Line 82: @@
 |<math>> f_{\omega+2}(f_{\omega+1}^2(3))</math>
 |<span style="word-break:break-all">{{TM|1RB1RA_1RI1RC_0LD1LG_0RE1LD_1LK1RF_1RG0RA_1RA0LH_1LG1LH_1RE0LJ_1LH1LI_1RZ0LL_0LH1LK|halt}}</span>
-|Jeff Ketchersid and Gemini in 2026 (claimed)
+|Jeff Ketchersid and Gemini in 10/2026 (claimed)
 |[https://github.com/jeff87654/busy-beaver/tree/main/BB12 Claimed analysis by Claude] never verified.
 |-
 |BB(13)
+|<math>> f_{\omega+2}^6(f_{\omega+1}^2(3))</math>
+|<span style="word-break:break-all">{{TM|1RB1RA_1RI1RC_0LD1LG_0RE1LD_1LK1RF_1RM0RA_1RA0LH_1LG1LH_1RE0LJ_1LH1LI_0LL0LL_0LH1LK_1RZ0LH|halt}}</span>
+|Jeff Ketchersid, Claude and Gemini in 10/2026 (claimed)
+|[https://github.com/jeff87654/busy-beaver/tree/main/BB13 Claimed analysis by Claude] never verified.
+|-
+|BB(14)
+|<math>> f_{\omega+3}(17)</math>
+|<span style="word-break:break-all">{{TM|1RB1RA_1RI1RC_0LD1LG_0RE1LD_1LK1RF_1RM0RA_1RA0LH_1LG1LH_1RE0LJ_1LH1LI_0LL0LL_0LN1LK_1RZ0LH_0LG1LJ|halt}}</span>
+|Jeff Ketchersid, Claude and Gemini in 11/2026 (claimed)
+|[https://github.com/jeff87654/busy-beaver/tree/main/BB14 Claimed analysis by Claude] never verified.
+|-
+|BB(15)
 |
 |
@@ Line 91: / Line 103: @@
 |
 |-
-|BB(14)
+|BB(16)
-|<math>> f_{\omega+2}^3(15)</math>
-|<span style="word-break:break-all">{{TM|1RB1RA_1RI1RC_0LD1LG_0RE1LD_1LN1RF_1LJ0RA_1RA0LH_1LG1LH_1RK0LM_1RZ0LE_0LE0RJ_1LH1LM_0LH0LL_0LG1LN|halt}}</span>
-|Jeff Ketchersid and Gemini in 2026 (claimed)
-|[https://github.com/jeff87654/busy-beaver/tree/main/BB14 Claimed analysis by Claude] never verified.
-|-
-|...
 |
 |
 |
 |
+|-
+|BB(17)
+|<math>> f_{\omega+3}^3(9)</math>
+|<span style="word-break:break-all">{{TM|1LB1LA_1RC0LA_1RD1RC_1RE1RK_1RF0LJ_1LG1RI_1RM0LM_1LG0RC_0RN0LE_1LA1LE_0LL1LB_0RM1LL_1LF1RH_1RQ0LO_1LP1LN_0RB1LI_1RZ1LO|halt}}</span>
+|Jeff Ketchersid, Claude and Gemini in 11/2026 (claimed)
+|[https://github.com/jeff87654/busy-beaver/tree/main/BB17 Claimed analysis by Claude] never verified.
+|-
+|BB(18)
+|<math>> f_{\omega+4}(228)</math>
+|<span style="word-break:break-all">{{TM|1LB1LA_1RC0LA_1RD1RC_1RE1RK_1RF0LJ_1LG1RI_1RM0LM_1LG0RC_0RN0LE_1LA1LE_0LL1LB_0RM1LL_1LF1RH_1RQ0LO_1LP1LR_0RB1LI_1RZ1RR_1RN0LO|halt}}</span>
+|Jeff Ketchersid, Claude and Gemini in 11/2026 (claimed)
+|[https://github.com/jeff87654/busy-beaver/tree/main/BB18 Claimed analysis by Claude] never verified.
+|-
+|BB(19)
+|<math>> f_{\omega + 7}^2(5)</math>
+|<span style="word-break:break-all">{{TM|1RQ1RL_0LI1RC_0LD1LF_0RA1LD_1RB1RE_1LH0LG_1LF1LG_1RE1RM_1LJ1LI_0LK1LI_1RL1RA_0RL0RE_0LN1RM_1LO0LO_1RE1LP_1LN1LN_1LR1RQ_1RZ1LS_0LE0LR|halt}}</span>
+|Jacobzheng in 2026
+|Not independently verified.
 |-
 |BB(20)
-|<math>> f_{\omega + 6}^2(4)</math>
+|<math>> f_{\omega \times 2}(f_{\omega + 2}^2(f_{10}(2)))</math>
-|<span style="word-break:break-all">{{TM|1RR---_0LJ0RC_1RB1LD_0LD1LE_1LF1RG_1LI0LE_0RE1LD_1RB1RH_1RH1RN_1LK1LJ_0LL1LJ_1RM1RA_0RM0RH_0LO1RN_1RH0LP_1RH1LQ_1RH1LO_1LS1RR_1RZ1LT_0LH0LS|halt}}</span>
+|<span style="word-break:break-all">{{TM|1LH0LG_0LI1RC_0LD1LA_0RE1LD_1RQ1RL_1RB1RF_1LA1LG_1RF1RM_1LJ1LI_0LK1LI_1RL1RE_0RL0RF_0LN1RM_0RF0LO_0RF1LP_0RF1LN_1LR1RQ_1RZ1LS_0LF1LT_0LF0LR|halt}}</span>
 |Jacobzheng in 2026
-|
+|Not independently verified.
 |-
 |BB(21)
@@ Line 113: / Line 137: @@
 |<span style="word-break:break-all">{{TM|0LI0LF_0RJ1RG_0RD1LC_1RH1RE_1LO0RH_1LA1LF_0LC1LA_1RB1RH_1RD0LF_1LP0RK_0LM1LL_0LL1LM_1LE1LN_0RQ0LM_0RP1LO_1LR0RH_1LF1RQ_1RZ0LS_1LH0LT_1LH1LU_0LE1LR|halt}}</span>
 |[https://discord.com/channels/960643023006490684/1026577255754903572/1274471360206344213 Racheline in 2024]
-|
+|Not independently verified.
+|-
+|colspan="5"|...
 |-
 |BB(29)
 |<math>> f_{\omega^\omega}(3)</math>
 |[https://github.com/jeff87654/busy-beaver/blob/main/BB29/hydra29.md]
-|mxdys in 2026 (claimed)
+|mxdys in 10/2026 (claimed)
 |[https://github.com/jeff87654/busy-beaver/tree/main/BB29 Claimed analysis by Claude] never verified.
 |-
@@ Line 124: / Line 150: @@
 |<math>> f_{\omega \uparrow \uparrow 4}(3)</math>
 |[https://github.com/jeff87654/busy-beaver/blob/main/BB31/hydra31.md]
-|mxdys in 2026 (claimed)
+|mxdys in 10/2026 (claimed)
 |[https://github.com/jeff87654/busy-beaver/tree/main/BB31 Claimed analysis by Claude] never verified.
 |-
@@ Line 130: / Line 156: @@
 |<math>> f_{\omega \uparrow \uparrow 6}(3)</math>
 |[https://github.com/jeff87654/busy-beaver/blob/main/BB33/hydra33.md]
-|mxdys in 2026 (claimed)
+|mxdys in 10/2026 (claimed)
 |[https://github.com/jeff87654/busy-beaver/tree/main/BB33 Claimed analysis by Claude] never verified.
 |-
-|BB(51)
+|BB(48)
-|<math>> f_{\varepsilon_0 + 1}(8)</math>
+|<math>> f_{\varepsilon_1}(3)</math>
-|[[Talk:Champions|See talk page]]
+|[https://discord.com/channels/960643023006490684/1331570843829932063/1567585091172040726]
-|[https://discord.com/channels/960643023006490684/1026577255754903572/1276881449685094495 Racheline in 2024]
+|[https://discord.com/channels/960643023006490684/1331570843829932063/1567585091172040726 roromachine14 and Gemini in 2026]
-|
+|Not independently verified.
 |-
 |BB(150)
@@ Line 143: / Line 169: @@
 |[https://morphett.info/turing/turing.html?c95a199c8e8a3dd56452f8b7e28fabbf too large to show]
 |Patcail in 2025<ref>https://discord.com/channels/960643023006490684/1026577255754903572/1328863966688182345</ref>
-|
+|Not independently verified.
 |-
 |BB(1015)
@@ Line 149: / Line 175: @@
 |
 |CatsAreFluffy in 2024<ref>https://github.com/CatsAreFluffy/metamath-turing-machines/commit/85948b04fc4aeb983ca6d63d6aee5ad6ef308bfe</ref>
-|
+|Not independently verified.
 |}
@@ Line 167: / Line 193: @@
 |[https://discord.com/channels/960643023006490684/1331570843829932063/1339669138510970881 racheline in 2025]
 |<math>q(n)</math> is derived from [https://en.wikipedia.org/wiki/Laver%20table Laver tables]. From [https://discord.com/channels/960643023006490684/960643023530762341/1525489299032641657 racheline]: "The known information about q(n) isn't enough to prove that this machine scores higher than the shown champions with fewer states, or that it scores lower than the shown champions with more states."
+If q(5) doesn't exist (this can only happen if [[Logical_independence|ZFC+I3 is inconsistent]]), then this machine doesn't halt.
 |}
@@ Line 195: / Line 222: @@
 |{{TM|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD|halt}}
 |Pavel Kropitz in 2024
-|
+|See Polygon's analysis on the TM page
 |-
 |BB(5,3)
@@ Line 207: / Line 234: @@
 |{{TM|1LE2LD2LC_2RB1RB1RA_2RB1LC0LC_1RB1LD2LD_2RD2LE2LF_1RZ---1LE|halt}}
 |Jacobzheng in 2026
-|
+|Not independently verified.
 |-
 |BB(7,3)
@@ Line 216: / Line 243: @@
 |-
 |BB(8,3)
-|<math>> f_{\omega+1}(f_\omega(f_7(2))) > g_{64}</math>
+|<math>> f_{\omega+1}(f_\omega^4(f_7(2))) > g_{64}</math>
-|<span style="word-break:break-all">{{TM|1LD1LE2RA_1RE2LE2RB_1RD2RA2LC_1RB1RD2RB_1LH2RF1LC_1RZ0LF1LG_1RD2LG2LG_0LD1LH1LH|halt}}</span>
+|<span style="word-break:break-all">{{TM|1RD2RE2LA_2RC2LC2RB_1LH2RF1LA_2RC1RD2RB_---1LC2RE_1RZ0LF1LG_1RD2LG2LG_0LA0LD1LH|halt}}</span>
 |Jacobzheng in 2026
-|
+|Not independently verified.
 |-
 |BB(9,3)
@@ Line 237: / Line 264: @@
 |<span style="word-break:break-all">{{TM|1LD2RG2LA_2LE2LH2RB_2LE1RC2RB_0RC1RD0LG_0LF1LE1LE_1RG1RI---_0RC1LH2RG_1RC2LH1LA_1RI1RI1LJ_0LA2LK---_1RZ2LJ---|halt}}</span>
 |Jacobzheng in 2026
-|
+|Not independently verified.
 |-
-|...
+|colspan="5"|...
-|
-|
-|
-|
 |-
 |BB(36,3)
@@ Line 249: / Line 272: @@
 |
 |Wythagoras in 2014<ref>https://googology.fandom.com/wiki/User:Wythagoras/Rado%27s_sigma_function/BB(36,3)</ref>
-|
+|Not independently verified.
 |-
 |BB(37,3)
@@ Line 255: / Line 278: @@
 |
 |Wythagoras in 2014<ref>https://googology.fandom.com/wiki/User:Wythagoras/Rado%27s_sigma_function/BB(37,3)</ref>
-|
+|Not independently verified.
 |}
@@ Line 283: / Line 306: @@
 |{{TM|0LB3LB1RZ2RA_1LD3RB1LC2RA_3RB1LB3LC2RC_0RD2RC2LB0RA|halt}}
 |[[User:Loader3229]] in 2026
-|Not independently verified.
+|[https://github.com/loader3229/busy-beaver/tree/main/BB44 Claimed analysis by MiniMax] Not independently verified.
 |-
 |BB(5,4)
@@ Line 289: / Line 312: @@
 |<span style="word-break:break-all">{{TM|1LD2RA3RB1LC_1LD2LA3RB---_2RA1LA3RC2LC_2RA---2LD2LE_------1RZ1LD|halt}}</span>
 |Jacobzheng in 2026
+|Not independently verified.
+|-
+|BB(6,4)
+|<math>> f_{\omega+1}(10\uparrow\uparrow 65\,533) > g_{64}</math>
+|<span style="word-break:break-all">{{TM|1LF2RA3RB---_3RD2LB3RB1LC_2RA1LB3RC2LC_1LD2RE0LA1LD_1RZ0LE1LF---_2RA---2LF2LF|halt}}</span>
+|Jacobzheng in 2026
+|Not independently verified.
+|-
+|BB(7,4)
+|
+|
+|
 |
 |-
-|[[BB(6,4)]]
+|BB(8,4)
-|<math>> f_{\omega+1}(40)</math>
+|<math>> f_{\omega+2}(f_\omega^4(12))</math>
-|<span style="word-break:break-all">{{TM|0LF3LB2RD2RA_2RF3RB1LC2RA_3RB1LB3LC2RC_1RZ2LD1LD2LE_3RE3LB2RE2LE_2LC0RA1LF1RB|halt}}</span>
+|<span style="word-break:break-all">{{TM|1RC3LB2RD2RA_1RF3RB1LC2RA_3RB1LB3LC2RC_0RF2LD1LD2LE_3RE3LB2RE2LE_0LG0LH1RZ3RB_1LG2RD1LG3RG_0LH0LC0LH3RD|halt}}</span>
+|[[User:Loader3229]] in 2026
+|Not independently verified.
+|-
+|BB(9,4)
+|<math>> f_{\omega+3}(16)</math>
+|<span style="word-break:break-all">{{TM|2LI3LB2RD2RA_2LC3RB1LC2RA_3RB1LB3LC2RC_0RF2LD1LD2LE_3RE3LB2RE2LE_0LG0LH1RZ---_1LG2RD1LG3RG_0LH---0LH3RD_2LB---1LI3RF|halt}}</span>
 |[[User:Loader3229]] in 2026
 |Not independently verified.
 |-
-|...
+|BB(10,4)
 |
 |
 |
 |
+|-
+|BB(11,4)
+|<math>> f_{\omega \times 2}(2 \uparrow^{11} 6)</math>
+|<span style="word-break:break-all">{{TM|1RK3LB1RZ2RA_0LG1LE1LD2RA_3RB1LB3LC2RC_3RE0LI3LC2RC_1RJ3RE3LH2LF_3RF2RF2LE1LF_3LC3LH2LJ2RG_0LE3RH1LI2RG_3RH1LH3LI2RI_0LB0LJ3LJ3RK_2LC0LD2RA3RK|halt}}</span>
+|[[User:Loader3229]] in 2026
+|Not independently verified.
+|-
+|colspan="5"|...
 |-
 |BB(31,4)
@@ Line 307: / Line 356: @@
 |
 |Wythagoras in 2014<ref>https://googology.fandom.com/wiki/User:Wythagoras/Rado%27s_sigma_function/BB(31,4)</ref>
-|
+|Not independently verified.
 |}
@@ Line 328: / Line 377: @@
 |{{TM|1RB3LB4LC2RA4LB_2LC3RB1LC2RA1RZ_3RB1LB3LC2RC4LC|halt}}
 |Racheline in 2024
-|
+|Not independently verified.
 |-
 |BB(4,5)
@@ Line 336: / Line 385: @@
 |Not independently verified.
 |-
-|...
+|BB(5,5)
-|
+|<math>> f_{\omega+1}(f_\omega^4(6))</math>
-|
+|{{TM|1LB3LB4LC2RA4LB_3LE3RB1LC2RA4RD_3RB1LB3LC2RC4LC_1RZ------4LD4LE_3RB------4LE3LC|halt}}
-|
+|[[User:Loader3229]] in 2026
-|
+|Not independently verified.
+|-
+|BB(6,5)
+|<math>> f_{\omega+3}(11)</math>
+|<span style="word-break:break-all">{{TM|2LE3LB4LC2RA4LB_4RA3RB1LC2RA4RD_3RB1LB3LC2RC4LC_1RZ3LF1LA4LD4LE_3RB---0RD4LE3LC_4LC------3LF3LF|halt}}</span>
+|[[User:Loader3229]] in 2026
+|Not independently verified.
+|-
+|BB(7,5)
+|<math>> f_{\omega+3}^2(10)</math>
+|<span style="word-break:break-all">{{TM|2LE3LB4LC2RA4LB_4RA3RB1LC2RA4RD_3RB1LB3LC2RC4LC_1RZ3LF1LG4LD4LE_3RB---1LE4LE3LC_4LC------3LF3LF_3LF------1LG1LG|halt}}</span>
+|[[User:Loader3229]] in 2026
+|Not independently verified.
+|-
+|BB(8,5)
+|<math>> f_{\omega \times 2+1}(93)</math>
+|<span style="word-break:break-all">{{TM|2RG3LB4LC2RA4LB_1RZ---1LD2RA4LD_3RB1LB3LC2RC4LC_3RE---3LC2RC3LC_---3RE4LE4LH4RB_4LE3LG3LB2RF4LG_2LH3RG1LH2RF2RA_3RG1LG3LH2RH4LH|halt}}</span>
+|[[User:Loader3229]] in 2026
+|Not independently verified.
+|-
+|colspan="5"|...
 |-
 |BB(19,5)
@@ Line 346: / Line 415: @@
 |<span style="word-break:break-all">{{TM|1RB2LA1RA2LB2LA_0LA2RB3RB4RA1LQ_1RZ1RC2LD------_0LK3RD2RD2RD4RD_------0RH1LS0RF_1LG1RF2RF---4RF_4LE1LG2LG---4LG_0LI1RH2RH---4RH_0RK0LJ------4RK_2LE1LJ2LJ---4LJ_4RP---0LE---0LK_2RQ---2LL---4LL_2LN---2RM3RM4RM_4RQ2RQ2LN3LN4LN_4LN---2RO3RO4RO_3LL1LP2LP1LQ4LP_1RC3RR1RM3LP0RO_3LL1RR2RR0RR4RR_1RC1LS2LS1LS4LS|halt}}</span>
 |Wythagoras in 2014<ref>https://googology.fandom.com/wiki/User:Wythagoras/Rado%27s_sigma_function/BB(19,5)</ref>
+|Not independently verified.
 |-
 |BB(94,5)
@@ Line 351: / Line 421: @@
 |
 |Wythagoras in 2014<ref>https://googology.fandom.com/wiki/User_blog:Wythagoras/Hydra_machines</ref>
-|
+|Not independently verified.
 |}
@@ Line 374: / Line 444: @@
 |Not independently verified.
 |-
-|...
+|BB(4,6)
-|
+|<math>> f_{\omega+2}(29)</math>
-|
+|{{TM|5LD3LB5LC2RA4LB4LC_1RZ3RB1LC2RA3RD0LA_3RB1LB3LC2RC4LC1RA_3RB0LA2LC4LD4LC4LD|halt}}
-|
+|[[User:Loader3229]] in 2026
-|
+|Not independently verified.
+|-
+|BB(5,6)
+|<math>> f_{\omega+3}(31)</math>
+|<span style="word-break:break-all">{{TM|1LE3LB2LA2RA4LB5RA_1RZ3RB1LC2RA3RD4RA_3RB1LB3LC2RC4LC2LB_3RB0LA5LE4LD4LC4LD_4LC5LC0RE5LE1RE2RE|halt}}</span>
+|[[User:Loader3229]] in 2026
+|Not independently verified.
+|-
+|BB(6,6)
+|<math>> f_{\omega \times 2}(89)</math>
+|<span style="word-break:break-all">{{TM|4LF3LB1RZ2RA4LB---_2LC3RB1LD2RA3LF---_3RB1LB3LC2RC4LC0LE_3RB---3LC2RC---3RE_5RC3RE---4LC------_5RB0LF1RB1LF---5RB|halt}}</span>
+|[[User:Loader3229]] in 2026
+|Not independently verified.
+|-
+|BB(7,6)
+|<math>> f_{\omega^2}(63)</math>
+|<span style="word-break:break-all">{{TM|2LE3LB1RZ2RA4LB2LD_0LA3RB1LD2RA3LF5RB_3RB1LB3LC2RC4LC1LE_3RB3RE3LC2RC---3RD_5RB3RE0LG4LC3LG5LE_5RB5RB---1LF---5LF_5LF---3RC1LG---5LG|halt}}</span>
+|[[User:Loader3229]] in 2026
+|Not independently verified.
+|-
+|BB(8,6)
+|<math>> f_{\omega^2+1}(7)</math>
+|<span style="word-break:break-all">{{TM|0LC3LB2LH2RA4LB1RZ_3LH3RB1LD2RA3LF5RB_3RB1LB3LC2RC4LC1LE_3RB3RE3LC2RC2LD3RD_5RB3RE---4LC3LG5LE_5RB5RB---1LF5LF5LF_5LF4RG1LB1LG5LD5LG_3LE---1LH1LH---5RG|halt}}</span>
+|[[User:Loader3229]] in 2026
+|Not independently verified.
+|-
+|colspan="5"|...
 |-
 |BB(61,6)
@@ Line 384: / Line 480: @@
 |
 |Wythagoras in 2014<ref>https://googology.fandom.com/wiki/User_blog:Wythagoras/Hydra_machines</ref>
-|
+|Not independently verified.
 |}
@@ Line 399: / Line 495: @@
 |{{TM|1RB3RB4LA1LB5LA6LB5RA_2LA6RA4RB1RZ3LB6LA4RB|halt}}
 |[https://discord.com/channels/960643023006490684/960643023530762341/1563057558011252761 roromachine14 in 2026]
-|
+|Not independently verified.
 |-
 |BB(3,7)
-|<math>> f_\omega^4(15)</math>
+|<math>> f_{\omega+1}(117) > g_{64}</math>
-|{{TM|1RB3LB4LC2RA4LB5LB6LB_2LC3RB1LC2RA5LC6LC1RZ_3RB1LB3LC2RC4LC5LC6LC|halt}}
+|{{TM|6LC3LB6RA2RA4LB5LC5LA_1RZ3RB1LC2RA3RB4LC5RA_3RB1LB3LC2RC4LC1RA6LA|halt}}
+|[[User:Loader3229]] in 2026
+|Not independently verified.
+|-
+|BB(4,7)
+|<math>> f_{\omega+3}(28)</math>
+|{{TM|5LC3LB0RD2RA4LB6LB1LC_1RZ3RB1LC2RA3RD2LC4LC_3RB1LB3LC2RC4LC1LA5LD_3RB6LA6LC4LD4LC4LD6LC|halt}}
 |[[User:Loader3229]] in 2026
 |Not independently verified.
 |-
-|...
+|colspan="5"|...
-|
-|
-|
-|
 |-
 |BB(18,7)
@@ Line 417: / Line 515: @@
 |<span style="word-break:break-all">{{TM|1RB2LA1RA2LB2LA------_0LA2RB3RB4RA1LP------_0RZ1RC2LD------------_0LJ3RD2RD2RD4RD------_4LE1LE0RG1LR0RF2LE4LE_1LE1RF5RF---6RF------_0LH1RG2RG---4RG------_0RJ0LI------4RJ------_2LE1LI2LI---4LI------_4RO---0LE---0LJ------_2RP---2LK---4LK------_2LM---2RL3RL4RL------_4RP2RP2LM3LM4LM------_4LM---2RN3RN4RN------_3LK1LO2LO1LP4LO------_1RC3RQ1RL3LO0RN------_3LK1RQ2RQ0RQ4RQ------_1RC1LR2LR1LR4LR------|halt}}</span>
 |Wythagoras in 2014<ref>https://googology.fandom.com/wiki/User:Wythagoras/Rado%27s_sigma_function/BB(18,7)</ref>
+|Not independently verified.
 |-
 |BB(46,7)
@@ Line 422: / Line 521: @@
 |
 |Wythagoras in 2014<ref>https://googology.fandom.com/wiki/User_blog:Wythagoras/Hydra_machines</ref>
-|
+|Not independently verified.
 |-
 |BB(134,7)
@@ Line 428: / Line 527: @@
 |
 |LittlePeng9+Wythagoras in 2014<ref>https://googology.fandom.com/wiki/User:Wythagoras/Rado%27s_sigma_function/Analysis_of_LittlePeng9%27s_work/Hydra_machines</ref>
-|
+|Not independently verified.
 |}
@@ Line 443: / Line 542: @@
 |{{TM|1RB3RB4LA1LB5LA6LB5RA1RZ_2LA6RA4RB7RA3LB6LA4RB4RA|halt}}
 |[https://discord.com/channels/960643023006490684/1084047886494470185/1563070360956698804 roromachine14 in 2026]
-|
-|-
-|BB(3,8)
-|<math>> f_\omega^5(15)</math>
-|{{TM|1RB3LB4LC2RA4LB5LB6LB7LB_2LC3RB1LC2RA5LC6LC7LC1RZ_3RB1LB3LC2RC4LC5LC6LC7LC|halt}}
-|[[User:Loader3229]] in 2026
 |Not independently verified.
 |-
-|...
+|colspan="5"|...
-|
-|
-|
-|
 |-
 |BB(17,8)
@@ Line 461: / Line 550: @@
 |<span style="word-break:break-all">{{TM|1RB2LA1RA2LB2LA---------_0LA2RB3RB4RA1LO---------_0RZ1RC2LD---------------_0LJ3RD2RD2RD4RD---------_4LE1LE0RG1LQ0RF2LE4LE---_1LE1RF5RF---6RF---------_0LH1RG2RG---4RG---------_0RJ0LI------4RJ---------_2LE1LI2LI---4LI---------_4RN---0LE---0LJ---------_2RO2RO2LK3LK4LK2LK4LK4RO_2LK---5RL3RL6RL---------_4LK---5RM3RM6RM---------_3LK1LN2LN1LO4LN---------_1RC3RP1RL3LN7RM---------_3LK1RP2RP0RP4RP---------_1RC1LQ2LQ1LQ4LQ---------|halt}}</span>
 |Wythagoras in 2014<ref>https://googology.fandom.com/wiki/User:Wythagoras/Rado%27s_sigma_function/BB(17,8)</ref>
-|
+|Not independently verified.
 |}
@@ Line 476: / Line 565: @@
 |{{TM|1RB3RB4LA1LB5LA6LB5RA8RA1RZ_2LA6RA4RB7RA3LB6LA4RB4RA4RA|halt}}
 |[https://discord.com/channels/960643023006490684/1084047886494470185/1563070360956698804 roromachine14 in 2026]
-|
-|-
-|BB(3,9)
-|<math>> f_\omega^6(15)</math>
-|<span style="word-break:break-all">{{TM|1RB3LB4LC2RA4LB5LB6LB7LB8LB_2LC3RB1LC2RA5LC6LC7LC8LC1RZ_3RB1LB3LC2RC4LC5LC6LC7LC8LC|halt}}</span>
-|[[User:Loader3229]] in 2026
 |Not independently verified.
 |-
-|...
+|colspan="5"|...
-|
-|
-|
-|
 |-
 |BB(42,9)
@@ Line 494: / Line 573: @@
 |
 |Wythagoras in 2014<ref>https://googology.fandom.com/wiki/User_blog:Wythagoras/Hydra_machines</ref>
-|
+|Not independently verified.
 |}
@@ Line 512: / Line 591: @@
 |
 * {{TM|1RZ---|halt}}
+* {{TM|0RA_0RZ|halt}}
+* {{TM|0RA_0RB_0RZ|halt}}
 |<math>O(n)</math>
 |-

Champions: Difference between revisions

Latest revision as of 10:48, 5 November 2026

Trivial Champions

2-Symbol TMs

Conjectured

3-Symbol TMs

4-Symbol TMs

5-Symbol TMs

6-Symbol TMs

7-Symbol TMs

8-Symbol TMs

9-Symbol TMs

Zoology

References

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