Beeping Busy Beaver - Revision history

Polygon: /* Champions */ added holdouts list for BBB(4)

2026-03-28T17:14:29Z

Champions: added holdouts list for BBB(4)

← Older revision		Revision as of 17:14, 28 March 2026
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	All known champions quasihalt by becoming [[Translated Cycler\|Translated Cyclers]], a property which is known to be weaker than the general quasihalting condition.		All known champions quasihalt by becoming [[Translated Cycler\|Translated Cyclers]], a property which is known to be weaker than the general quasihalting condition.

			For BBB(4), 3713 holdouts remain ([https://wiki.bbchallenge.org/w/images/6/62/BBB4_holdouts_3713.txt list]).

	==Beeping Booping Busy Beavers==		==Beeping Booping Busy Beavers==

Polygon: /* Champions */ added BBB(1) champion

2025-12-25T12:48:03Z

Champions: added BBB(1) champion

← Older revision		Revision as of 12:48, 25 December 2025
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	\|BBB(1)		\|BBB(1)
	\|1<ref name=":0" />		\|1<ref name=":0" />
	\|		\|{{TM\|1RZ---\|halt}}
	\|-		\|-
	\|BBB(2)		\|BBB(2)

Polygon: /* Champions */ organised champions into a table

2025-12-25T12:46:10Z

Champions: organised champions into a table

← Older revision		Revision as of 12:46, 25 December 2025
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	== Champions ==		== Champions ==
			{\| class="wikitable"
	* BBB(1) = 1<ref name=":0" />		\|+
	* BBB(2) = 6<ref name=":0" /> by {{TM\|1RB1LB_1LB1LA}}		!Domain
	* BBB(3) = 55 by {{TM\|1RB0LB_1LA0RC_1LC1LA}}		!Steps
	* BBB(4) ≥ 32,779,478 by {{TM\|1RB1LD_1RC1RB_1LC1LA_0RC0RD}}		!Champions
	* BBB(5) > 10<sup>14,006</sup><ref>Nick Drozd. https://scottaaronson.blog/?p=8088#comment-1981333</ref> by {{TM\|1RB1LE_0LC0LB_0LD1LC_1RD1RA_0RC0LA}} ~~and probably <math>BBB(5) > 10^{10^{10^5}}</math> due to four "[[probviously]]" quasihalting [[Cryptids]].<ref>Shawn Ligocki. 2022. [https://www.sligocki.com/2022/04/03/mother-of~~-~~giants.html Mother of Giants].</ref>~~		\|-
			\|BBB(1)
	*BBB(2,3) = 59<ref>Nick Drozd. "[https://nickdrozd.github.io/2025/03/24/bbb-3-3.html BBB(3,3) > 10↑↑6]". Accessed 15 August 2025.</ref> by {{TM\|1RB2LB1LA_2LB2RA0RA}}		\|1<ref name=":0" />
	*BBB(3,3) > 10 ↑↑ 6<ref>https://groups.google.com/g/busy-beaver-discuss/c/EuIXSir4Eps</ref> by {{TM\|1RB0LB2LA_1LA0RC0LB_2RC2RB0LC}}		\|
	*BBB(2,4) > <math>2 \times 10^{23}</math><ref>Nick Drozd. "[https://nickdrozd.github.io/2022/02/11/latest-beeping-busy-beaver-results.html Latest Beeping Busy Beaver Results]". Accessed 15 August 2025.</ref> by {{TM\|1RB2LA1RA1LB_0LB2RB3RB1LA}}		\|-
			\|BBB(2)
			\|6<ref name=":0" />
			\|{{TM\|1RB1LB_1LB1LA}}
			\|-
			\|BBB(3)
			\|55
			\|{{TM\|1RB0LB_1LA0RC_1LC1LA}}
			\|-
			\|BBB(4)
			\|≥ 32,779,478
			\|{{TM\|1RB1LD_1RC1RB_1LC1LA_0RC0RD}}
			\|-
			\|BBB(5)*
			\|> 10<sup>14,006</sup><ref>Nick Drozd. https://scottaaronson.blog/?p=8088#comment-1981333</ref>
			\|{{TM\|1RB1LE_0LC0LB_0LD1LC_1RD1RA_0RC0LA}}
			\|-
			\|BBB(2,3)
			\|59<ref>Nick Drozd. "[https://nickdrozd.github.io/2025/03/24/bbb-3-3.html BBB(3,3) > 10↑↑6]". Accessed 15 August 2025.</ref>
			\|{{TM\|1RB2LB1LA_2LB2RA0RA}}
			\|-
			\|BBB(3,3)
			\|> 10 ↑↑ 6<ref>https://groups.google.com/g/busy-beaver-discuss/c/EuIXSir4Eps</ref>
			\|{{TM\|1RB0LB2LA_1LA0RC0LB_2RC2RB0LC}}
			\|-
			\|BBB(2,4)
			\|> <math>2 \times 10^{23}</math><ref>Nick Drozd. "[https://nickdrozd.github.io/2022/02/11/latest-beeping-busy-beaver-results.html Latest Beeping Busy Beaver Results]". Accessed 15 August 2025.</ref>
			\|{{TM\|1RB2LA1RA1LB_0LB2RB3RB1LA}}
			\|}
			<nowiki>*</nowiki> probably <math>BBB(5) > 10^{10^{10^5}}</math> due to four "[[probviously]]" quasihalting [[Cryptids]].<ref>Shawn Ligocki. 2022. [https://www.sligocki.com/2022/04/03/mother-of-giants.html Mother of Giants].</ref>

	All known champions quasihalt by becoming [[Translated Cycler\|Translated Cyclers]], a property which is known to be weaker than the general quasihalting condition.		All known champions quasihalt by becoming [[Translated Cycler\|Translated Cyclers]], a property which is known to be weaker than the general quasihalting condition.

Polygon: /* Results */ changed heading + spacing fix

2025-12-25T11:42:50Z

Results: changed heading + spacing fix

← Older revision		Revision as of 11:42, 25 December 2025
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	etc.		etc.

	== ~~Results~~ ==		== Champions ==

	* BBB(1) = 1<ref name=":0" />		* BBB(1) = 1<ref name=":0" />
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	*BBB(2,3) = 59<ref>Nick Drozd. "[https://nickdrozd.github.io/2025/03/24/bbb-3-3.html BBB(3,3) > 10↑↑6]". Accessed 15 August 2025.</ref> by {{TM\|1RB2LB1LA_2LB2RA0RA}}		*BBB(2,3) = 59<ref>Nick Drozd. "[https://nickdrozd.github.io/2025/03/24/bbb-3-3.html BBB(3,3) > 10↑↑6]". Accessed 15 August 2025.</ref> by {{TM\|1RB2LB1LA_2LB2RA0RA}}
	*BBB(3,3) > ~~10↑↑6~~<ref>https://groups.google.com/g/busy-beaver-discuss/c/EuIXSir4Eps</ref> by {{TM\|1RB0LB2LA_1LA0RC0LB_2RC2RB0LC}}		*BBB(3,3) > 10 ↑↑ 6<ref>https://groups.google.com/g/busy-beaver-discuss/c/EuIXSir4Eps</ref> by {{TM\|1RB0LB2LA_1LA0RC0LB_2RC2RB0LC}}
	*BBB(2,4) > <math>2 \times 10^{23}</math><ref>Nick Drozd. "[https://nickdrozd.github.io/2022/02/11/latest-beeping-busy-beaver-results.html Latest Beeping Busy Beaver Results]". Accessed 15 August 2025.</ref> by {{TM\|1RB2LA1RA1LB_0LB2RB3RB1LA}}		*BBB(2,4) > <math>2 \times 10^{23}</math><ref>Nick Drozd. "[https://nickdrozd.github.io/2022/02/11/latest-beeping-busy-beaver-results.html Latest Beeping Busy Beaver Results]". Accessed 15 August 2025.</ref> by {{TM\|1RB2LA1RA1LB_0LB2RB3RB1LA}}

Polygon: /* Results */ These are approximations

2025-09-23T19:50:35Z

Results: These are approximations

← Older revision		Revision as of 19:50, 23 September 2025
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	* BBB(3) = 55 by {{TM\|1RB0LB_1LA0RC_1LC1LA}}		* BBB(3) = 55 by {{TM\|1RB0LB_1LA0RC_1LC1LA}}
	* BBB(4) ≥ 32,779,478 by {{TM\|1RB1LD_1RC1RB_1LC1LA_0RC0RD}}		* BBB(4) ≥ 32,779,478 by {{TM\|1RB1LD_1RC1RB_1LC1LA_0RC0RD}}
	* BBB(5) ≥ 10<sup>14,006</sup><ref>Nick Drozd. https://scottaaronson.blog/?p=8088#comment-1981333</ref> by {{TM\|1RB1LE_0LC0LB_0LD1LC_1RD1RA_0RC0LA}} and probably <math>BBB(5) ~~\ge~~ 10^{10^{10^5}}</math> due to four "[[probviously]]" quasihalting [[Cryptids]].<ref>Shawn Ligocki. 2022. [https://www.sligocki.com/2022/04/03/mother-of-giants.html Mother of Giants].</ref>		* BBB(5) > 10<sup>14,006</sup><ref>Nick Drozd. https://scottaaronson.blog/?p=8088#comment-1981333</ref> by {{TM\|1RB1LE_0LC0LB_0LD1LC_1RD1RA_0RC0LA}} and probably <math>BBB(5) > 10^{10^{10^5}}</math> due to four "[[probviously]]" quasihalting [[Cryptids]].<ref>Shawn Ligocki. 2022. [https://www.sligocki.com/2022/04/03/mother-of-giants.html Mother of Giants].</ref>

	*BBB(2,3) = 59<ref>Nick Drozd. "[https://nickdrozd.github.io/2025/03/24/bbb-3-3.html BBB(3,3) > 10↑↑6]". Accessed 15 August 2025.</ref> by {{TM\|1RB2LB1LA_2LB2RA0RA}}		*BBB(2,3) = 59<ref>Nick Drozd. "[https://nickdrozd.github.io/2025/03/24/bbb-3-3.html BBB(3,3) > 10↑↑6]". Accessed 15 August 2025.</ref> by {{TM\|1RB2LB1LA_2LB2RA0RA}}
	*BBB(3,3) ≥ 10↑↑6<ref>https://groups.google.com/g/busy-beaver-discuss/c/EuIXSir4Eps</ref> by {{TM\|1RB0LB2LA_1LA0RC0LB_2RC2RB0LC}}		*BBB(3,3) > 10↑↑6<ref>https://groups.google.com/g/busy-beaver-discuss/c/EuIXSir4Eps</ref> by {{TM\|1RB0LB2LA_1LA0RC0LB_2RC2RB0LC}}
	*BBB(2,4) > <math>2 \times 10^{23}</math><ref>Nick Drozd. "[https://nickdrozd.github.io/2022/02/11/latest-beeping-busy-beaver-results.html Latest Beeping Busy Beaver Results]". Accessed 15 August 2025.</ref> by {{TM\|1RB2LA1RA1LB_0LB2RB3RB1LA}}		*BBB(2,4) > <math>2 \times 10^{23}</math><ref>Nick Drozd. "[https://nickdrozd.github.io/2022/02/11/latest-beeping-busy-beaver-results.html Latest Beeping Busy Beaver Results]". Accessed 15 August 2025.</ref> by {{TM\|1RB2LA1RA1LB_0LB2RB3RB1LA}}

Int-y1: rename heading

2025-09-23T03:13:35Z

rename heading

← Older revision		Revision as of 03:13, 23 September 2025
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	Note that these Turing machines need not ever halt, so the [[Tree Normal Form]] algorithm needs to be modified (to allow TMs with no halt transitions) when searching for BBB champions.		Note that these Turing machines need not ever halt, so the [[Tree Normal Form]] algorithm needs to be modified (to allow TMs with no halt transitions) when searching for BBB champions.

	== ~~Significance~~ ==		== Growth rate ==

	It is easy to see that <math>\operatorname{BBB}(n) \ge \operatorname{BB}(n)</math>, by letting the beep state be the state that is reached immediately before the halt state.		It is easy to see that <math>\operatorname{BBB}(n) \ge \operatorname{BB}(n)</math>, by letting the beep state be the state that is reached immediately before the halt state.

Polygon: /* Results */ Added BBB(2,3) champion and used TNF-1RB for BBB(3)

2025-09-22T19:26:53Z

Results: Added BBB(2,3) champion and used TNF-1RB for BBB(3)

← Older revision		Revision as of 19:26, 22 September 2025
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	* BBB(1) = 1<ref name=":0" />		* BBB(1) = 1<ref name=":0" />
	* BBB(2) = 6<ref name=":0" /> by {{TM\|1RB1LB_1LB1LA}}		* BBB(2) = 6<ref name=":0" /> by {{TM\|1RB1LB_1LB1LA}}
	* BBB(3) = 55 by {{TM\|~~1LB0RB_1RA0LC_1RC1RA~~}}		* BBB(3) = 55 by {{TM\|1RB0LB_1LA0RC_1LC1LA}}
	* BBB(4) ≥ 32,779,478 by {{TM\|1RB1LD_1RC1RB_1LC1LA_0RC0RD}}		* BBB(4) ≥ 32,779,478 by {{TM\|1RB1LD_1RC1RB_1LC1LA_0RC0RD}}
	* BBB(5) ≥ 10<sup>14,006</sup><ref>Nick Drozd. https://scottaaronson.blog/?p=8088#comment-1981333</ref> by {{TM\|1RB1LE_0LC0LB_0LD1LC_1RD1RA_0RC0LA}} and probably <math>BBB(5) \ge 10^{10^{10^5}}</math> due to four "[[probviously]]" quasihalting [[Cryptids]].<ref>Shawn Ligocki. 2022. [https://www.sligocki.com/2022/04/03/mother-of-giants.html Mother of Giants].</ref>		* BBB(5) ≥ 10<sup>14,006</sup><ref>Nick Drozd. https://scottaaronson.blog/?p=8088#comment-1981333</ref> by {{TM\|1RB1LE_0LC0LB_0LD1LC_1RD1RA_0RC0LA}} and probably <math>BBB(5) \ge 10^{10^{10^5}}</math> due to four "[[probviously]]" quasihalting [[Cryptids]].<ref>Shawn Ligocki. 2022. [https://www.sligocki.com/2022/04/03/mother-of-giants.html Mother of Giants].</ref>

	*BBB(2,3) = 59<ref>Nick Drozd. "[https://nickdrozd.github.io/2025/03/24/bbb-3-3.html BBB(3,3) > 10↑↑6]". Accessed 15 August 2025.</ref>		*BBB(2,3) = 59<ref>Nick Drozd. "[https://nickdrozd.github.io/2025/03/24/bbb-3-3.html BBB(3,3) > 10↑↑6]". Accessed 15 August 2025.</ref> by {{TM\|1RB2LB1LA_2LB2RA0RA}}
	*BBB(3,3) ≥ 10↑↑6<ref>https://groups.google.com/g/busy-beaver-discuss/c/EuIXSir4Eps</ref> by {{TM\|1RB0LB2LA_1LA0RC0LB_2RC2RB0LC}}		*BBB(3,3) ≥ 10↑↑6<ref>https://groups.google.com/g/busy-beaver-discuss/c/EuIXSir4Eps</ref> by {{TM\|1RB0LB2LA_1LA0RC0LB_2RC2RB0LC}}
	*BBB(2,4) > <math>2 \times 10^{23}</math><ref>Nick Drozd. "[https://nickdrozd.github.io/2022/02/11/latest-beeping-busy-beaver-results.html Latest Beeping Busy Beaver Results]". Accessed 15 August 2025.</ref> by {{TM\|1RB2LA1RA1LB_0LB2RB3RB1LA}}		*BBB(2,4) > <math>2 \times 10^{23}</math><ref>Nick Drozd. "[https://nickdrozd.github.io/2022/02/11/latest-beeping-busy-beaver-results.html Latest Beeping Busy Beaver Results]". Accessed 15 August 2025.</ref> by {{TM\|1RB2LA1RA1LB_0LB2RB3RB1LA}}

Racheline: /* Beeping Booping Busy Beavers */ mentioned three specific models of BBBB, and included the values for 1-state and 2-state (2-symbol) BBBB

2025-09-17T15:00:47Z

Beeping Booping Busy Beavers: mentioned three specific models of BBBB, and included the values for 1-state and 2-state (2-symbol) BBBB

← Older revision		Revision as of 15:00, 17 September 2025
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	==Beeping Booping Busy Beavers==		==Beeping Booping Busy Beavers==
	An extension devised by Bram Cohen goes as follows: a Turing machine has two special transitions, a beep transition and a boop transition, both of which repeat infinitely often. The machine outputs an integer sequence corresponding to the number of beeps between successive boops. The machine's number is the number of transitions it takes to finish the first output value that is repeated infinitely many times. These machines are considered equivalent to Turing machines with second-order oracles.<ref>Bram Cohen. 2023. [https://bramcohen.com/p/beeping-booping-busy-beavers Beeping Booping Busy Beavers].</ref>		An extension devised by Bram Cohen goes as follows: a Turing machine has two special transitions, a beep transition and a boop transition, both of which repeat infinitely often. The machine outputs an integer sequence corresponding to the number of beeps between successive boops. The machine's number is the number of transitions it takes to finish the first output value that is repeated infinitely many times. These machines are considered equivalent to Turing machines with second-order oracles.<ref>Bram Cohen. 2023. [https://bramcohen.com/p/beeping-booping-busy-beavers Beeping Booping Busy Beavers].</ref>

			There are multiple models to choose from, depending on whether one allows multiple beep transitions and multiple boop transitions, or only one of each, or only one boop transition while making every transition a beep transition. All of these models have the same computational strength and corresponding growth rate, but each has its own advantages. The first is the most general, including all machines from the other two, and in that sense it is more natural, but that makes the space of candidate machines to search through significantly larger. The second is the original definition and it is relatively simple. The third is equivalent to simply considering the amount of time between successive boops, instead of the number of beeps between successive boops, and has the smallest space of candidate machines. It is not yet decided which of these models (or perhaps a model different from all three) should be chosen for "the" BBBB function.

			It is known that for all three of these models, BBBB(1) = 2 and BBBB(2) = 17.<ref>[https://discord.com/channels/960643023006490684/1243312334907375676/1417836470793670697 Discord message]</ref>

	== References ==		== References ==

	[[category:Functions]]		[[category:Functions]]

Polygon: /* Results */ Mother of giants actually are four cryptids

2025-08-28T17:05:41Z

Results: Mother of giants actually are four cryptids

← Older revision		Revision as of 17:05, 28 August 2025
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	* BBB(3) = 55 by {{TM\|1LB0RB_1RA0LC_1RC1RA}}		* BBB(3) = 55 by {{TM\|1LB0RB_1RA0LC_1RC1RA}}
	* BBB(4) ≥ 32,779,478 by {{TM\|1RB1LD_1RC1RB_1LC1LA_0RC0RD}}		* BBB(4) ≥ 32,779,478 by {{TM\|1RB1LD_1RC1RB_1LC1LA_0RC0RD}}
	* BBB(5) ≥ 10<sup>14,006</sup><ref>Nick Drozd. https://scottaaronson.blog/?p=8088#comment-1981333</ref> by {{TM\|1RB1LE_0LC0LB_0LD1LC_1RD1RA_0RC0LA}} and probably <math>BBB(5) \ge 10^{10^{10^5}}</math> due to a "[[probviously]]" quasihalting [[Cryptids~~\|Cryptid~~]].<ref>Shawn Ligocki. 2022. [https://www.sligocki.com/2022/04/03/mother-of-giants.html Mother of Giants].</ref>		* BBB(5) ≥ 10<sup>14,006</sup><ref>Nick Drozd. https://scottaaronson.blog/?p=8088#comment-1981333</ref> by {{TM\|1RB1LE_0LC0LB_0LD1LC_1RD1RA_0RC0LA}} and probably <math>BBB(5) \ge 10^{10^{10^5}}</math> due to four "[[probviously]]" quasihalting [[Cryptids]].<ref>Shawn Ligocki. 2022. [https://www.sligocki.com/2022/04/03/mother-of-giants.html Mother of Giants].</ref>

	*BBB(2,3) = 59<ref>Nick Drozd. "[https://nickdrozd.github.io/2025/03/24/bbb-3-3.html BBB(3,3) > 10↑↑6]". Accessed 15 August 2025.</ref>		*BBB(2,3) = 59<ref>Nick Drozd. "[https://nickdrozd.github.io/2025/03/24/bbb-3-3.html BBB(3,3) > 10↑↑6]". Accessed 15 August 2025.</ref>

Polygon: /* Results */ Changed score of BBB(2,4) champion, the old one might have been a typo

2025-08-15T17:03:45Z

Results: Changed score of BBB(2,4) champion, the old one might have been a typo

← Older revision		Revision as of 17:03, 15 August 2025
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	* BBB(5) ≥ 10<sup>14,006</sup><ref>Nick Drozd. https://scottaaronson.blog/?p=8088#comment-1981333</ref> by {{TM\|1RB1LE_0LC0LB_0LD1LC_1RD1RA_0RC0LA}} and probably <math>BBB(5) \ge 10^{10^{10^5}}</math> due to a "[[probviously]]" quasihalting [[Cryptids\|Cryptid]].<ref>Shawn Ligocki. 2022. [https://www.sligocki.com/2022/04/03/mother-of-giants.html Mother of Giants].</ref>		* BBB(5) ≥ 10<sup>14,006</sup><ref>Nick Drozd. https://scottaaronson.blog/?p=8088#comment-1981333</ref> by {{TM\|1RB1LE_0LC0LB_0LD1LC_1RD1RA_0RC0LA}} and probably <math>BBB(5) \ge 10^{10^{10^5}}</math> due to a "[[probviously]]" quasihalting [[Cryptids\|Cryptid]].<ref>Shawn Ligocki. 2022. [https://www.sligocki.com/2022/04/03/mother-of-giants.html Mother of Giants].</ref>

	*BBB(2,3) = 59<ref ~~name=":1"~~>Nick Drozd. "[https://nickdrozd.github.io/2025/03/24/bbb-3-3.html BBB(3,3) > 10↑↑6]". Accessed 15 August 2025</ref>		*BBB(2,3) = 59<ref>Nick Drozd. "[https://nickdrozd.github.io/2025/03/24/bbb-3-3.html BBB(3,3) > 10↑↑6]". Accessed 15 August 2025.</ref>
	*BBB(3,3) ≥ 10↑↑6<ref>https://groups.google.com/g/busy-beaver-discuss/c/EuIXSir4Eps</ref> by {{TM\|1RB0LB2LA_1LA0RC0LB_2RC2RB0LC}}		*BBB(3,3) ≥ 10↑↑6<ref>https://groups.google.com/g/busy-beaver-discuss/c/EuIXSir4Eps</ref> by {{TM\|1RB0LB2LA_1LA0RC0LB_2RC2RB0LC}}
	*BBB(2,4) > <math>10^{24}</math><ref ~~name=~~":1" />		*BBB(2,4) > <math>2 \times 10^{23}</math><ref>Nick Drozd. "[https://nickdrozd.github.io/2022/02/11/latest-beeping-busy-beaver-results.html Latest Beeping Busy Beaver Results]". Accessed 15 August 2025.</ref> by {{TM\|1RB2LA1RA1LB_0LB2RB3RB1LA}}

	All known champions quasihalt by becoming [[Translated Cycler\|Translated Cyclers]], a property which is known to be weaker than the general quasihalting condition.		All known champions quasihalt by becoming [[Translated Cycler\|Translated Cyclers]], a property which is known to be weaker than the general quasihalting condition.

← Older revision		Revision as of 19:50, 23 September 2025
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	* BBB(3) = 55 by {{TM\|1RB0LB_1LA0RC_1LC1LA}}		* BBB(3) = 55 by {{TM\|1RB0LB_1LA0RC_1LC1LA}}
	* BBB(4) ≥ 32,779,478 by {{TM\|1RB1LD_1RC1RB_1LC1LA_0RC0RD}}		* BBB(4) ≥ 32,779,478 by {{TM\|1RB1LD_1RC1RB_1LC1LA_0RC0RD}}
	* BBB(5) ≥ 10<sup>14,006</sup><ref>Nick Drozd. https://scottaaronson.blog/?p=8088#comment-1981333</ref> by {{TM\|1RB1LE_0LC0LB_0LD1LC_1RD1RA_0RC0LA}} and probably <math>BBB(5) ~~\ge~~ 10^{10^{10^5}}</math> due to four "[[probviously]]" quasihalting [[Cryptids]].<ref>Shawn Ligocki. 2022. [https://www.sligocki.com/2022/04/03/mother-of-giants.html Mother of Giants].</ref>		* BBB(5) > 10<sup>14,006</sup><ref>Nick Drozd. https://scottaaronson.blog/?p=8088#comment-1981333</ref> by {{TM\|1RB1LE_0LC0LB_0LD1LC_1RD1RA_0RC0LA}} and probably <math>BBB(5) > 10^{10^{10^5}}</math> due to four "[[probviously]]" quasihalting [[Cryptids]].<ref>Shawn Ligocki. 2022. [https://www.sligocki.com/2022/04/03/mother-of-giants.html Mother of Giants].</ref>

	*BBB(2,3) = 59<ref>Nick Drozd. "[https://nickdrozd.github.io/2025/03/24/bbb-3-3.html BBB(3,3) > 10↑↑6]". Accessed 15 August 2025.</ref> by {{TM\|1RB2LB1LA_2LB2RA0RA}}		*BBB(2,3) = 59<ref>Nick Drozd. "[https://nickdrozd.github.io/2025/03/24/bbb-3-3.html BBB(3,3) > 10↑↑6]". Accessed 15 August 2025.</ref> by {{TM\|1RB2LB1LA_2LB2RA0RA}}
	*BBB(3,3) ≥ 10↑↑6<ref>https://groups.google.com/g/busy-beaver-discuss/c/EuIXSir4Eps</ref> by {{TM\|1RB0LB2LA_1LA0RC0LB_2RC2RB0LC}}		*BBB(3,3) > 10↑↑6<ref>https://groups.google.com/g/busy-beaver-discuss/c/EuIXSir4Eps</ref> by {{TM\|1RB0LB2LA_1LA0RC0LB_2RC2RB0LC}}
	*BBB(2,4) > <math>2 \times 10^{23}</math><ref>Nick Drozd. "[https://nickdrozd.github.io/2022/02/11/latest-beeping-busy-beaver-results.html Latest Beeping Busy Beaver Results]". Accessed 15 August 2025.</ref> by {{TM\|1RB2LA1RA1LB_0LB2RB3RB1LA}}		*BBB(2,4) > <math>2 \times 10^{23}</math><ref>Nick Drozd. "[https://nickdrozd.github.io/2022/02/11/latest-beeping-busy-beaver-results.html Latest Beeping Busy Beaver Results]". Accessed 15 August 2025.</ref> by {{TM\|1RB2LA1RA1LB_0LB2RB3RB1LA}}

← Older revision		Revision as of 19:26, 22 September 2025
Line 26:		Line 26:
	* BBB(1) = 1<ref name=":0" />		* BBB(1) = 1<ref name=":0" />
	* BBB(2) = 6<ref name=":0" /> by {{TM\|1RB1LB_1LB1LA}}		* BBB(2) = 6<ref name=":0" /> by {{TM\|1RB1LB_1LB1LA}}
	* BBB(3) = 55 by {{TM\|~~1LB0RB_1RA0LC_1RC1RA~~}}		* BBB(3) = 55 by {{TM\|1RB0LB_1LA0RC_1LC1LA}}
	* BBB(4) ≥ 32,779,478 by {{TM\|1RB1LD_1RC1RB_1LC1LA_0RC0RD}}		* BBB(4) ≥ 32,779,478 by {{TM\|1RB1LD_1RC1RB_1LC1LA_0RC0RD}}
	* BBB(5) ≥ 10<sup>14,006</sup><ref>Nick Drozd. https://scottaaronson.blog/?p=8088#comment-1981333</ref> by {{TM\|1RB1LE_0LC0LB_0LD1LC_1RD1RA_0RC0LA}} and probably <math>BBB(5) \ge 10^{10^{10^5}}</math> due to four "[[probviously]]" quasihalting [[Cryptids]].<ref>Shawn Ligocki. 2022. [https://www.sligocki.com/2022/04/03/mother-of-giants.html Mother of Giants].</ref>		* BBB(5) ≥ 10<sup>14,006</sup><ref>Nick Drozd. https://scottaaronson.blog/?p=8088#comment-1981333</ref> by {{TM\|1RB1LE_0LC0LB_0LD1LC_1RD1RA_0RC0LA}} and probably <math>BBB(5) \ge 10^{10^{10^5}}</math> due to four "[[probviously]]" quasihalting [[Cryptids]].<ref>Shawn Ligocki. 2022. [https://www.sligocki.com/2022/04/03/mother-of-giants.html Mother of Giants].</ref>

	*BBB(2,3) = 59<ref>Nick Drozd. "[https://nickdrozd.github.io/2025/03/24/bbb-3-3.html BBB(3,3) > 10↑↑6]". Accessed 15 August 2025.</ref>		*BBB(2,3) = 59<ref>Nick Drozd. "[https://nickdrozd.github.io/2025/03/24/bbb-3-3.html BBB(3,3) > 10↑↑6]". Accessed 15 August 2025.</ref> by {{TM\|1RB2LB1LA_2LB2RA0RA}}
	*BBB(3,3) ≥ 10↑↑6<ref>https://groups.google.com/g/busy-beaver-discuss/c/EuIXSir4Eps</ref> by {{TM\|1RB0LB2LA_1LA0RC0LB_2RC2RB0LC}}		*BBB(3,3) ≥ 10↑↑6<ref>https://groups.google.com/g/busy-beaver-discuss/c/EuIXSir4Eps</ref> by {{TM\|1RB0LB2LA_1LA0RC0LB_2RC2RB0LC}}
	*BBB(2,4) > <math>2 \times 10^{23}</math><ref>Nick Drozd. "[https://nickdrozd.github.io/2022/02/11/latest-beeping-busy-beaver-results.html Latest Beeping Busy Beaver Results]". Accessed 15 August 2025.</ref> by {{TM\|1RB2LA1RA1LB_0LB2RB3RB1LA}}		*BBB(2,4) > <math>2 \times 10^{23}</math><ref>Nick Drozd. "[https://nickdrozd.github.io/2022/02/11/latest-beeping-busy-beaver-results.html Latest Beeping Busy Beaver Results]". Accessed 15 August 2025.</ref> by {{TM\|1RB2LA1RA1LB_0LB2RB3RB1LA}}