BB(5) - Revision history

F-string: Remove orphaned bullet point from previous edit

2026-10-27T20:23:12Z

Remove orphaned bullet point from previous edit

← Older revision		Revision as of 20:23, 27 October 2026
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	* In 2021, all BB(5) TMs were enumerated in TNF<ref>https://bbchallenge.org/method#seed-database</ref> and a database of undecided TMs was established.<ref>Downloadable seed database. https://docs.bbchallenge.org/all_5_states_undecided_machines_with_global_header.zip</ref>		* In 2021, all BB(5) TMs were enumerated in TNF<ref>https://bbchallenge.org/method#seed-database</ref> and a database of undecided TMs was established.<ref>Downloadable seed database. https://docs.bbchallenge.org/all_5_states_undecided_machines_with_global_header.zip</ref>
	* In 2022, [[bbchallenge.org]] was released, with the aim of collaboratively proving that BB(5) = 47,176,870.<ref>https://bbchallenge.org/story</ref>		* In 2022, [[bbchallenge.org]] was released, with the aim of collaboratively proving that BB(5) = 47,176,870.<ref>https://bbchallenge.org/story</ref>
	* In
	* In 2024, bbchallenge's contributor @mxdys published [[Coq-BB5]], a Rocq-verified proof of BB(5) = 47,176,870<ref name=":4">https://github.com/ccz181078/Coq-BB5</ref>, ending a 60-year-old quest. This proof uses and/or improves on many other bbchallenge's contributions.		* In 2024, bbchallenge's contributor @mxdys published [[Coq-BB5]], a Rocq-verified proof of BB(5) = 47,176,870<ref name=":4">https://github.com/ccz181078/Coq-BB5</ref>, ending a 60-year-old quest. This proof uses and/or improves on many other bbchallenge's contributions.

HelpMe: conflict

2026-10-08T17:17:06Z

conflict

← Older revision		Revision as of 17:17, 8 October 2026
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	\| style="background: #FFCCCC;" \|≥ 13		\| style="background: #FFCCCC;" \|≥ 13
	\|Lee, C. Y<ref>https://etd.ohiolink.edu/acprod/odb_etd/etd/r/1501/10?clear=10&p10_accession_num=osu1486567232687544</ref>		\|Lee, C. Y<ref>https://etd.ohiolink.edu/acprod/odb_etd/etd/r/1501/10?clear=10&p10_accession_num=osu1486567232687544</ref>
	\|Eventually proven (informally) to be a Σ(4) champion in ~~1974~~.		\|Eventually proven (informally) to be a Σ(4) champion in 1983.
	\|-		\|-
	\|October 1966		\|October 1966
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	\| style="background: #FFCCCC;" \|≥ 13		\| style="background: #FFCCCC;" \|≥ 13
	\|Brady, A.<ref name=":12">Brady, A. H. (1966). The Conjectured Highest Scoring Machines for Rado's Σ(k) for the Value k = 4. https://ieeexplore.ieee.org/document/4038890</ref>		\|Brady, A.<ref name=":12">Brady, A. H. (1966). The Conjectured Highest Scoring Machines for Rado's Σ(k) for the Value k = 4. https://ieeexplore.ieee.org/document/4038890</ref>
	\|Eventually proven (informally) to be the S(4) and a Σ(4) champion in ~~1974~~.		\|Eventually proven (informally) to be the S(4) and a Σ(4) champion in 1983.
	\|-		\|-
	\| rowspan="2" \|August 1972		\| rowspan="2" \|August 1972

HelpMe: splitting

2026-10-07T16:20:53Z

splitting

← Older revision		Revision as of 16:20, 7 October 2026
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	\|≥ 992		\|≥ 992
	\| style="background: #FFCCCC;" \|≥ 23		\| style="background: #FFCCCC;" \|≥ 23
	\| rowspan="2" \|Weimann, B.<ref name=":5">https://docs.bbchallenge.org/other/lud20.pdf</ref>		\| rowspan="2" \|Weimann, B.<ref name=":5">https://docs.bbchallenge.org/other/lud20.pdf</ref>
	\| rowspan="2" \|These bounds were published simultaneously.		\| rowspan="2" \|These bounds were published simultaneously.
	\|-		\|-
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	\|≥ 11,798,826		\|≥ 11,798,826
	\|≥ 4,098		\|≥ 4,098
	\| rowspan="3" \|Marxen, H., Buntrock, J.<ref name=":0" />		\| rowspan="3" \|Marxen, H., Buntrock, J.<ref name=":0" />
	\|Eventually proven to be an Σ(5) champion in 2024.		\|Eventually proven to be an Σ(5) champion in 2024.
	\|-		\|-
	\| rowspan="2" \|September 1989		\| rowspan="2" \|September 1989
	\|{{TM\|1RB0LD_1LC1RD_1LA1LC_1RZ1RE_1RA0RB\|halt}}		\|{{TM\|1RB0LD_1LC1RD_1LA1LC_1RZ1RE_1RA0RB\|halt}}
	\|≥ 23,554,764		\|≥ 23,554,764
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	\|-		\|-
	\|June 2024		\|June 2024
	\|'''= 47,176,870'''		\|'''= 47,176,870'''
	\|'''= 4,098'''		\|'''= 4,098'''
	\|bbchallenge<ref name=":4" />		\|bbchallenge<ref name=":4" />
	\|The bbchallenge proved S(5) = 47,176,870 and Σ(5) = 4,098 using [[Coq-BB5]].		\|The bbchallenge proved S(5) = 47,176,870 and Σ(5) = 4,098 using [[Coq-BB5]].
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	* In 2021, all BB(5) TMs were enumerated in TNF<ref>https://bbchallenge.org/method#seed-database</ref> and a database of undecided TMs was established.<ref>Downloadable seed database. https://docs.bbchallenge.org/all_5_states_undecided_machines_with_global_header.zip</ref>		* In 2021, all BB(5) TMs were enumerated in TNF<ref>https://bbchallenge.org/method#seed-database</ref> and a database of undecided TMs was established.<ref>Downloadable seed database. https://docs.bbchallenge.org/all_5_states_undecided_machines_with_global_header.zip</ref>
	* In 2022, [[bbchallenge.org]] was released, with the aim of collaboratively proving that BB(5) = 47,176,870.<ref>https://bbchallenge.org/story</ref>		* In 2022, [[bbchallenge.org]] was released, with the aim of collaboratively proving that BB(5) = 47,176,870.<ref>https://bbchallenge.org/story</ref>
			* In
	* In 2024, bbchallenge's contributor @mxdys published [[Coq-BB5]], a Rocq-verified proof of BB(5) = 47,176,870<ref name=":4">https://github.com/ccz181078/Coq-BB5</ref>, ending a 60-year-old quest. This proof uses and/or improves on many other bbchallenge's contributions.		* In 2024, bbchallenge's contributor @mxdys published [[Coq-BB5]], a Rocq-verified proof of BB(5) = 47,176,870<ref name=":4">https://github.com/ccz181078/Coq-BB5</ref>, ending a 60-year-old quest. This proof uses and/or improves on many other bbchallenge's contributions.

HelpMe: actually this is a better way of stating it

2026-10-07T15:28:44Z

actually this is a better way of stating it

Show changes

Loader3229: /* History */

2026-10-07T12:30:18Z

History

← Older revision		Revision as of 12:30, 7 October 2026
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	\|They did not prove (or claim) that this machine is the actual winner (i.e. that no other 5-state machines halt after more steps) but they presented some ideas for automatically deciding the behavior of Turing machines (i.e. making [[Deciders]]).		\|They did not prove (or claim) that this machine is the actual winner (i.e. that no other 5-state machines halt after more steps) but they presented some ideas for automatically deciding the behavior of Turing machines (i.e. making [[Deciders]]).
	Eventually proven to be the S(5) champion and an Σ(5) champion in 2024.		Eventually proven to be the S(5) champion and an Σ(5) champion in 2024.
			\|-
			\|June 2024
			\|{{TM\|1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA\|halt}}
			\|= 47,176,870
			\|= 4,098
			\|mxdys and bbchallenge
			\|The bbchallenge proved S(5) = 47,176,870 and Σ(5) = 4,098 using [[Coq-BB5]].
	\|}		\|}

HelpMe: okay maybe this format is better for inheriting champions

2026-09-28T14:09:12Z

okay maybe this format is better for inheriting champions

← Older revision		Revision as of 14:09, 28 September 2026
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	== History ==		== History ==
	In this section, we use Radó's original S (number of steps) and Σ (number of ones on the final tape) notations, see [[Busy Beaver Functions\|Busy beaver functions]].		In this section, we use Radó's original S (number of steps) and Σ (number of ones on the final tape) notations, see [[Busy Beaver Functions\|Busy beaver functions]].
	{\| class="wikitable mw-collapsible"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+		\|+
	! colspan="6" \|Timeline of lower bounds established for Σ(5) and S(5)<ref name=":1">Pascal Michel. (2022). The Busy Beaver Competition: a historical survey. https://bbchallenge.org/~pascal.michel/ha#tm52 </ref>		! colspan="6" \|Timeline of lower bounds established for Σ(5) and S(5)<ref name=":1">Pascal Michel. (2022). The Busy Beaver Competition: a historical survey. https://bbchallenge.org/~pascal.michel/ha#tm52 </ref>
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	\|?		\|?
	\|Mentioned by Green, M., mentioned by Lynn, D.<ref name=":3">https://docs.bbchallenge.org/papers/Lynn1972.pdf</ref>		\|Mentioned by Green, M., mentioned by Lynn, D.<ref name=":3">https://docs.bbchallenge.org/papers/Lynn1972.pdf</ref>
	~~Step count unknown~~.		Green, M. did not state the machine which showed this bound.
	\|-		\|-
	\|November 1964		\|November 1964
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	\|Green, M.		\|Green, M.
	\|Part of an infinite family of machines now known as [[Green's machines]].		\|Part of an infinite family of machines now known as [[Green's machines]].
	During this period, the steps champion ~~might have been~~ different to the ones champion.		During this period, the steps champion was different to the ones champion.
			\|-
			\|December 1964 - August 1972
			\|various
			\|≥ 84 - 107
			\|(≥ 11 - 13)
			\|Brady, A.<ref>Brady, A. H. (1965). Solutions of restricted cases of the halting problem applied to the determination of particular values of a non-computable function. <nowiki>https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/zk51vk21c</nowiki></ref><ref>https://ieeexplore.ieee.org/document/4038890</ref>
			Lee, C. Y.<ref>https://etd.ohiolink.edu/acprod/odb_etd/etd/r/1501/10?clear=10&p10_accession_num=osu1486567232687544</ref>
			\|During this period, the steps champion was inherited from [[BB(4)]], and was different to the ones champion.
	\|-		\|-
	\| rowspan="2" \|August 1972		\| rowspan="2" \|August 1972
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	\| rowspan="2" \|Lynn, D.<ref>https://docs.bbchallenge.org/papers/Brady1983.pdf</ref>		\| rowspan="2" \|Lynn, D.<ref>https://docs.bbchallenge.org/papers/Brady1983.pdf</ref>
	\| rowspan="2" \|During this period, the steps champion was different to the ones champion.		\| rowspan="2" \|During this period, the steps champion was different to the ones champion.
	~~Bounds were published in 1983.~~		These bounds were published simultaneously in April 1983.

	These bounds were published simultaneously.
	\|-		\|-
	\|{{TM\|1RB0LE_1RC0RA_1LD1RZ_1LE1LD_1LA0LC\|halt}}		\|{{TM\|1RB0LE_1RC0RA_1LD1RZ_1LE1LD_1LA0LC\|halt}}

HelpMe: fixed citations, decided to change green machine to original form, fixed 1974S

2026-09-25T14:26:44Z

fixed citations, decided to change green machine to original form, fixed 1974S

← Older revision		Revision as of 14:26, 25 September 2026
Line 12:		Line 12:
	== History ==		== History ==
	In this section, we use Radó's original S (number of steps) and Σ (number of ones on the final tape) notations, see [[Busy Beaver Functions\|Busy beaver functions]].		In this section, we use Radó's original S (number of steps) and Σ (number of ones on the final tape) notations, see [[Busy Beaver Functions\|Busy beaver functions]].
	{\| class="wikitable"		{\| class="wikitable mw-collapsible"
	\|+		\|+
	! colspan="6" \|Timeline of lower bounds established for Σ(5) and S(5)		! colspan="6" \|Timeline of lower bounds established for Σ(5) and S(5)<ref name=":1">Pascal Michel. (2022). The Busy Beaver Competition: a historical survey. https://bbchallenge.org/~pascal.michel/ha#tm52 </ref>
	\|-		\|-
	!Month of discovery		!Month of discovery
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	\|≥ 17		\|≥ 17
	\|?		\|?
	\|Mentioned by Green, M., mentioned by ~~Brady~~, A.<ref name=":3">https://docs.bbchallenge.org/papers/~~Brady1965~~.pdf</ref>		\|Mentioned by Green, M., mentioned by Lynn, D.<ref name=":3">https://docs.bbchallenge.org/papers/Lynn1972.pdf</ref>
	Step count unknown.		Step count unknown.
	\|-		\|-
	\|November 1964		\|November 1964
	\|{{TM\|~~1RD1RB_1RZ1RA_0RB1RD_0RE0RD_1LE1LC~~\|halt}}		\|{{TM\|1LD1LB_1LZ1LA_0LB1LD_0LE0LD_1RE1RC\|halt}}
	\|≥ 79		\|≥ 79
	\|(≥ 13)		\|(≥ 13)
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	\|≥ 435		\|≥ 435
	\|(≥ 15)		\|(≥ 15)
	\| rowspan="2" \|Lynn, D.<ref name=":4"~~>https:~~/~~/docs.bbchallenge.org/papers/Lynn1972.pdf</ref~~>		\| rowspan="2" \|Lynn, D.<ref name=":3" />
	\| rowspan="2" \|During this period, the steps champion was different to the ones champion.		\| rowspan="2" \|During this period, the steps champion was different to the ones champion.
			These bounds were published simultaneously.
	\|-		\|-
	\|{{TM\|1RB1RC_1LC1LD_0RA1LB_1RE0LB_1RZ1RD\|halt}}		\|{{TM\|1RB1RC_1LC1LD_0RA1LB_1RE0LB_1RZ1RD\|halt}}
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	\| rowspan="2" \|Weimann, B.<ref name=":5">https://docs.bbchallenge.org/other/lud20.pdf</ref>		\| rowspan="2" \|Weimann, B.<ref name=":5">https://docs.bbchallenge.org/other/lud20.pdf</ref>
	\| rowspan="2" \|During this period, the steps champion was different to the ones champion.		\| rowspan="2" \|During this period, the steps champion was different to the ones champion.
			These bounds were published simultaneously.
	\|-		\|-
	\|{{TM\|1RB1RA_1RC0RB_1LD1LC_1LE0LC_0RA1RZ\|halt}}		\|{{TM\|1RB1RA_1RC0RB_1LD1LC_1LE0LC_0RA1RZ\|halt}}
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	\|-		\|-
	\| rowspan="2" \|1974		\| rowspan="2" \|1974
	\|{{TM\|~~1RB0LC_1RC0RD_1LA0LC_1RD1RE_0RA1RZ~~\|halt}}		\|{{TM\|0RB1RZ_1RC0LD_1RD0RE_1LB0LD_1RE1RA\|halt}}
	\|≥ 7,~~706~~		\|≥ 7,707
	\|(≥ 88)		\|(≥ 88)
	\| rowspan="2" \|Lynn, D.<ref ~~name="~~:3" />		\| rowspan="2" \|Lynn, D.<ref>https://docs.bbchallenge.org/papers/Brady1983.pdf</ref>
	\| rowspan="2" \|~~Lynn's stopping convention for these machines seems to return a stopping value one greater than the modern stopping convention.~~		\| rowspan="2" \|During this period, the steps champion was different to the ones champion.
	During this period, the steps champion was different to the ones champion.		Bounds were published in 1983.

	~~Bounds~~ were ~~only~~ published ~~in 1983~~.		These bounds were published simultaneously.
	\|-		\|-
	\|{{TM\|1RB0LE_1RC0RA_1LD1RZ_1LE1LD_1LA0LC\|halt}}		\|{{TM\|1RB0LE_1RC0RA_1LD1RZ_1LE1LD_1LA0LC\|halt}}
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	\|≥ 501		\|≥ 501
	\|Schult, U.<ref name=":5" />		\|Schult, U.<ref name=":5" />
	\|In 1983, the [https://docs.bbchallenge.org/other/lud20.pdf Dortmund contest] was organised to find new 5-state [[champions]]. Uwe Schult won with this machine.		\|In 1983, the [https://docs.bbchallenge.org/other/lud20.pdf Dortmund contest] was organised to find new 5-state [[champions]]; Uwe Schult won with this machine.
	\|-		\|-
	\|December 1984		\|December 1984
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	\|≥ 2,133,492		\|≥ 2,133,492
	\|≥ 1,915		\|≥ 1,915
	\| rowspan="2" \|Uhing, G.<ref ~~name="~~:~~1">Pascal Michel~~. ~~(2022)~~. ~~The Busy Beaver Competition: a historical survey~~. https://bbchallenge.org/~~~pascal~~.~~michel/ha#tm52~~ </ref>		\| rowspan="2" \|Uhing, G.<ref>https://docs.bbchallenge.org/papers/Dewdney1984.pdf</ref><ref>https://docs.bbchallenge.org/papers/Brady1988.pdf</ref>
	\|		\|Bound was published by 1985.
	\|-		\|-
	\|February 1986		\|February 1986
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	\|≥ 4,098		\|≥ 4,098
	\| rowspan="3" \|Marxen, H., Buntrock, J.<ref name=":0" />		\| rowspan="3" \|Marxen, H., Buntrock, J.<ref name=":0" />
	\|Eventually proven to be ~~one of the~~ Σ(5) ~~champions~~ in 2024.		\|Eventually proven to be an Σ(5) champion in 2024.
	\|-		\|-
	\| rowspan="2" \|September 1989		\| rowspan="2" \|September 1989
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	\|(≥ 4,098)		\|(≥ 4,098)
	\|They did not prove (or claim) that this machine is the actual winner (i.e. that no other 5-state machines halt after more steps) but they presented some ideas for automatically deciding the behavior of Turing machines (i.e. making [[Deciders]]).		\|They did not prove (or claim) that this machine is the actual winner (i.e. that no other 5-state machines halt after more steps) but they presented some ideas for automatically deciding the behavior of Turing machines (i.e. making [[Deciders]]).
	Eventually proven to be the S(5) champion and ~~one of the~~ Σ(5) ~~champions~~ in 2024.		Eventually proven to be the S(5) champion and an Σ(5) champion in 2024.
	\|}		\|}

HelpMe: maybe did a rewrite of the top. \

2026-09-19T15:29:04Z

maybe did a rewrite of the top. \

← Older revision		Revision as of 15:29, 19 September 2026
Line 1:		Line 1:
	The 5-state, 2-symbol Busy Beaver problem, '''BB(5)''', refers to the 5<sup>th</sup> value of the [[Busy Beaver function]]. In September 1989, the [[5-state busy beaver winner]] was found: a 5-state [[Turing machine]] halting after 47,176,870 steps giving the lower bound BB(5) ≥ 47,176,870.<ref name=":0">H. Marxen and J. Buntrock. Attacking the Busy Beaver 5. Bulletin of the EATCS, 40, pages 247-251, February 1990. https://turbotm.de/~heiner/BB/mabu90.html</ref>		The 5-state, 2-symbol Busy Beaver problem, '''BB(5)''', refers to the 5<sup>th</sup> value of the [[Busy Beaver function]]. In September 1989, the [[5-state busy beaver winner]] was found: a 5-state [[Turing machine]] halting after 47,176,870 steps giving the lower bound BB(5) ≥ 47,176,870.<ref name=":0">H. Marxen and J. Buntrock. Attacking the Busy Beaver 5. Bulletin of the EATCS, 40, pages 247-251, February 1990. https://turbotm.de/~heiner/BB/mabu90.html</ref>

	~~In 2024,~~ BB(5) ~~= 47~~,~~176,870 was proven~~ by the [[bbchallenge.org]] massively collaborative research project.<ref name=":2">Determination of the fifth Busy Beaver value. bbchallenge Collaboration et. al. https://arxiv.org/abs/2509.12337</ref>		The BB(5) champion {{TM\|1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA\|halt}} and a Σ(5) champion {{TM\|1RB1RA_1LC1LB_1RA1LD_1RA1LE_1RZ0LC\|halt}}, were discovered in 1989 by Heiner Marxen and Jürgen Buntrock. These machines were shown to be the definite champions in 2024 by the [[bbchallenge.org]] massively collaborative research project<ref name=":2">Determination of the fifth Busy Beaver value. bbchallenge Collaboration et. al. https://arxiv.org/abs/2509.12337</ref>, proving:

			<math display="block">\begin{array}{lcrl}
			\operatorname{BB}(5) & = & 47,176,870 \\
			\Sigma(5) & = & 4,098 \\
			\end{array}</math>

	BB(5) is the only BB Domain to have [[Irregular Turing Machine\|irregular TMs]] without also having [[Cryptids]].		BB(5) is the only BB Domain to have [[Irregular Turing Machine\|irregular TMs]] without also having [[Cryptids]].

	== History ==		== History ==
	In this ~~Section~~, we use Radó's original S (number of steps) and Σ (number of ones on the final tape) notations, see [[Busy Beaver Functions]].		In this section, we use Radó's original S (number of steps) and Σ (number of ones on the final tape) notations, see [[Busy Beaver Functions\|Busy beaver functions]].
	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+
Line 49:		Line 54:
	\|≥ 992		\|≥ 992
	\|(≥ 23)		\|(≥ 23)
	\| rowspan="2" \|Weimann, B.<ref>https://docs.bbchallenge.org/other/lud20.pdf</ref>		\| rowspan="2" \|Weimann, B.<ref name=":5">https://docs.bbchallenge.org/other/lud20.pdf</ref>
	\| rowspan="2" \|During this period, the steps champion was different to the ones champion.		\| rowspan="2" \|During this period, the steps champion was different to the ones champion.
	\|-		\|-
Line 74:		Line 79:
	\|≥ 134,467		\|≥ 134,467
	\|≥ 501		\|≥ 501
	\|Schult, U.<ref name=":4" />		\|Schult, U.<ref name=":5" />
	\|In 1983, the [https://docs.bbchallenge.org/other/lud20.pdf Dortmund contest] was organised to find new 5-state [[champions]]. Uwe Schult won with this machine.		\|In 1983, the [https://docs.bbchallenge.org/other/lud20.pdf Dortmund contest] was organised to find new 5-state [[champions]]. Uwe Schult won with this machine.
	\|-		\|-

HelpMe: did updates. we still need know the sigma 17

2026-09-19T14:39:23Z

did updates. we still need know the sigma 17

← Older revision		Revision as of 14:39, 19 September 2026
Line 9:		Line 9:
	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+
	! colspan="6" \|Timeline of lower bounds established for Σ(5) and S(5)<ref name=":PMH">Pascal Michel. (last updated 2026). The Busy Beaver Competition: a historical survey. https://bbchallenge.org/~pascal.michel/ha#tm62</ref><ref name=":1">Pascal Michel. (2022). The Busy Beaver Competition: a historical survey. https://bbchallenge.org/~pascal.michel/ha#tm52 </ref>		! colspan="6" \|Timeline of lower bounds established for Σ(5) and S(5)
	\|-		\|-
	!Month of discovery		!Month of discovery
Line 23:		Line 23:
	\|≥ 17		\|≥ 17
	\|?		\|?
	\|Mentioned by Green, M., mentioned by Brady, A.<ref>https://docs.bbchallenge.org/papers/Brady1965.pdf</ref>		\|Mentioned by Green, M., mentioned by Brady, A.<ref name=":3">https://docs.bbchallenge.org/papers/Brady1965.pdf</ref>
	Step count unknown.		Step count unknown.
	\|-		\|-
Line 38:		Line 38:
	\|≥ 435		\|≥ 435
	\|(≥ 15)		\|(≥ 15)
	\| rowspan="2" \|Lynn, D.		\| rowspan="2" \|Lynn, D.<ref name=":4">https://docs.bbchallenge.org/papers/Lynn1972.pdf</ref>
	\| rowspan="2" \|During this period, the steps champion was different to the ones champion.		\| rowspan="2" \|During this period, the steps champion was different to the ones champion.
	\|-		\|-
Line 45:		Line 45:
	\|≥ 22		\|≥ 22
	\|-		\|-
	\|~~October~~ 1973		\| rowspan="2" \|November 1973
	\|		\|{{TM\|1RB0LD_1RC0RB_1LA0RA_0LC0LE_1LC1RZ\|halt}}
	\|≥ 556		\|≥ 992
			\|(≥ 23)
			\| rowspan="2" \|Weimann, B.<ref>https://docs.bbchallenge.org/other/lud20.pdf</ref>
			\| rowspan="2" \|During this period, the steps champion was different to the ones champion.
			\|-
			\|{{TM\|1RB1RA_1RC0RB_1LD1LC_1LE0LC_0RA1RZ\|halt}}
			\|(≥ 556)
	\|≥ 40		\|≥ 40
	~~\|Weimann, B.~~
	~~\|TODO: Find machine in <ref>https://docs.bbchallenge.org/papers/WeimannCasperFenzl1973.pdf</ref>, because the editor can't read German.~~
	\|-		\|-
	\| rowspan="2" \|1974		\| rowspan="2" \|1974
Line 56:		Line 60:
	\|≥ 7,706		\|≥ 7,706
	\|(≥ 88)		\|(≥ 88)
	\| rowspan="2" \|Lynn, D.		\| rowspan="2" \|Lynn, D.<ref name=":3" />
	\| rowspan="2" \|Lynn's stopping convention for these machines seems to return a stopping value one greater than the modern stopping convention.		\| rowspan="2" \|Lynn's stopping convention for these machines seems to return a stopping value one greater than the modern stopping convention.
	During this period, the steps champion was different to the ones champion.		During this period, the steps champion was different to the ones champion.

	Bounds were only published in 1983.		Bounds were only published in 1983.
	\|-		\|-
Line 69:		Line 74:
	\|≥ 134,467		\|≥ 134,467
	\|≥ 501		\|≥ 501
	\|Schult, U,		\|Schult, U.<ref name=":4" />
	\|In 1983, the [https://docs.bbchallenge.org/other/lud20.pdf Dortmund contest] was organised to find new 5-state [[champions]]. Uwe Schult won with this machine.		\|In 1983, the [https://docs.bbchallenge.org/other/lud20.pdf Dortmund contest] was organised to find new 5-state [[champions]]. Uwe Schult won with this machine.
	\|-		\|-
Line 76:		Line 81:
	\|≥ 2,133,492		\|≥ 2,133,492
	\|≥ 1,915		\|≥ 1,915
	\| rowspan="2" \|Uhing, G.		\| rowspan="2" \|Uhing, G.<ref name=":1">Pascal Michel. (2022). The Busy Beaver Competition: a historical survey. https://bbchallenge.org/~pascal.michel/ha#tm52 </ref>
	\|		\|
	\|-		\|-
Line 89:		Line 94:
	\|≥ 11,798,826		\|≥ 11,798,826
	\|≥ 4,098		\|≥ 4,098
	\| rowspan="3" \|Marxen, H., Buntrock, J.		\| rowspan="3" \|Marxen, H., Buntrock, J.<ref name=":0" />
	\|Eventually proven to be one of the Σ(5) champions in 2024.		\|Eventually proven to be one of the Σ(5) champions in 2024.
	\|-		\|-
Line 101:		Line 106:
	\|≥ 47,176,870		\|≥ 47,176,870
	\|(≥ 4,098)		\|(≥ 4,098)
	\|They did not prove (or claim) that this machine is the actual winner (i.e. that no other 5-state machines halt after more steps) but they presented some ideas for automatically deciding the behavior of Turing machines (i.e. making [[Deciders]]).~~<ref name=":0" />~~		\|They did not prove (or claim) that this machine is the actual winner (i.e. that no other 5-state machines halt after more steps) but they presented some ideas for automatically deciding the behavior of Turing machines (i.e. making [[Deciders]]).
	Eventually proven to be the S(5) champion and one of the Σ(5) champions in 2024.		Eventually proven to be the S(5) champion and one of the Σ(5) champions in 2024.
	\|}		\|}

HelpMe: table the BB(5) step and number ones. two to find

2026-09-19T13:27:20Z

table the BB(5) step and number ones. two to find

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