User:Azerty/Busy Beaver Functions

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

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

I will add more functions soon.

Turing Machines

Function	Lower Bound	Champion
BB(2)	6	1RB1LB_1LA1RZ (bbch)
BB(3)	21	1RB1RZ_1LB0RC_1LC1LA (bbch)
BB(2,3)	38	1RB2LB1RZ_2LA2RB1LB (bbch)
BB(4)	107	1RB1LB_1LA0LC_1RZ1LD_1RD0RA (bbch)
BB(2,4)	3,932,964	1RB2LA1RA1RA_1LB1LA3RB1RZ (bbch)
BB(5)	47,176,870	1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA (bbch)
BB(3,3)	$>1.191\times 10^{17}$	0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC (bbch)
BB(2,5)	$>10^{10^{10^{3314360}}}$	1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ (bbch)
BB(2,6)	$>10{\uparrow }^{2}10{\uparrow }^{2}10^{10^{115}}$	1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA (bbch)
BB(6)	$>10{\uparrow }^{2}10{\uparrow }^{2}10{\uparrow }^{2}8$	1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE (bbch)
BB(4,3)	$>10{\uparrow }^{3}10{\uparrow }^{3}10{\uparrow }^{3}10^{28}$	1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD (bbch)
BB(7)	$>10{\uparrow }^{11}10{\uparrow }^{10}4$	1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch)
BB(3,4)	$>10{\uparrow }^{15}4$	1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC (bbch)
BB(3,5)	$>f_{\omega }(10{\uparrow }^{15}4)$	1RB3LB4LC2RA4LB_2LC3RB1LC2RA1RZ_3RB1LB3LC2RC4LC (bbch)