User:Polygon/Collection of BB Champions - Revision history

Polygon: /* Regular Busy Beaver for Lambda Calculus (BBλ(n)) */ updated BBlambda(38) to proven

2026-04-26T08:40:16Z

Regular Busy Beaver for Lambda Calculus (BBλ(n)): updated BBlambda(38) to proven

← Older revision		Revision as of 08:40, 26 April 2026
Line 1,090:		Line 1,090:
	\|-		\|-
	\|BBλ(38)		\|BBλ(38)
	\|<math>~~\geq~~ 5 \times 2^{2^{2^{2^{2}}}} +6 > 10^{19729}</math>		\|<math> 5 \times 2^{2^{2^{2^{2}}}} +6 > 10^{19729}</math>
	\|<math>(\lambda 1 1 1 1 1) (\lambda\lambda 2 (2 1))</math>		\|<math>(\lambda 1 1 1 1 1) (\lambda\lambda 2 (2 1))</math>
	\|-		\|-

Polygon: /* Fractran (BBf(n)) */ updated BBf(20) to proven

2026-04-26T08:39:30Z

Fractran (BBf(n)): updated BBf(20) to proven

← Older revision		Revision as of 08:39, 26 April 2026
Line 1,537:		Line 1,537:
	\|-		\|-
	\|20		\|20
	\|≥ 746		\| 746
	\|<code>[7/15, 22/3, 6/77, 5/2, 9/5]</code>		\|<code>[7/15, 22/3, 6/77, 5/2, 9/5]</code>
	\|<math>\begin{bmatrix}		\|<math>\begin{bmatrix}
Line 1,548:		Line 1,548:
	\|-		\|-
	\|21		\|21
	\|≥ 31,957,632		\|≥ 31,957,632
	\|<code>[7/15, 4/3, 27/14, 5/2, 9/5]</code>		\|<code>[7/15, 4/3, 27/14, 5/2, 9/5]</code>
	\|<math>\begin{bmatrix}		\|<math>\begin{bmatrix}

Polygon: /* Blanking Busy Beaver (BLB(n,m)) */ added BLB(7)

2026-04-02T17:49:27Z

Blanking Busy Beaver (BLB(n,m)): added BLB(7)

← Older revision		Revision as of 17:49, 2 April 2026
Line 537:		Line 537:
	\|≥ 65,538,549<ref>Comment #62 "https://scottaaronson.blog/?p=5661". Accessed 26 September 2025.</ref>		\|≥ 65,538,549<ref>Comment #62 "https://scottaaronson.blog/?p=5661". Accessed 26 September 2025.</ref>
	\|{{TM\|1RB1LE_1RD1RB_0RD0RE_1LD1LA_0RF1RF_0LC1LC}}		\|{{TM\|1RB1LE_1RD1RB_0RD0RE_1LD1LA_0RF1RF_0LC1LC}}
			\|-
			\|BLB(7)
			\|> 10^183.76332<ref>https://discord.com/channels/960643023006490684/1369339127652159509/1374531970830307409</ref>
			\|{{TM\|1RB0RF_1RC1RA_1LD0LA_0RG0RE_0RA1LF_0LE0LC_1RZ0RD\|halt}}
	\|}		\|}
	{\| class="wikitable"		{\| class="wikitable"

Polygon: /* Busy Beaver for De Bruijn Lambda Calculus */ updated n = 14

2026-03-29T17:13:42Z

Busy Beaver for De Bruijn Lambda Calculus: updated n = 14

← Older revision		Revision as of 17:13, 29 March 2026
Line 1,314:		Line 1,314:
	\|-		\|-
	\|14		\|14
	\|<math>> 10 {\~~uparrow~~}^{3} ~~10 {~~\~~uparrow}^{3} 10 {~~\~~uparrow}^{3} 16~~</math>		\|<math>> f_{\omega}\left(f_{5}\left(2\right)\right)</math>
	\|<code>(\~~1 1~~ 1 1 1) (\1 (\\2 (2 1)) 1)</code>		\|<code>(\1 1 1) (\\1 (1 2) (\\2 (2 1)))</code>
	\|-		\|-
	\|15		\|15

Polygon: /* Cyclic Tag (CTBB(n)) */ added Tiny Tag

2026-02-28T10:49:19Z

Cyclic Tag (CTBB(n)): added Tiny Tag

@@ Line 1,597: / Line 1,597: @@
 |<u>></u> 4↑↑↑↑(4↑↑↑3)<ref>https://discord.com/channels/960643023006490684/1438694294042181742/1442950825545564281</ref> <ref>https://discord.com/channels/960643023006490684/1438694294042181742/1442819117735346217</ref>
+|
 |}

Polygon: /* Regular Busy Beaver for Lambda Calculus (BBλ(n)) */ updated laver table champion

2026-02-17T20:39:50Z

Regular Busy Beaver for Lambda Calculus (BBλ(n)): updated laver table champion

← Older revision		Revision as of 20:39, 17 February 2026
Line 1,161:		Line 1,161:
	\|<math>(\lambda 1 1 (\lambda 1 (\lambda\lambda\lambda\lambda 1 4 4 4 3 2 1) 1 1 1 1) 1) (\lambda\lambda 2 (2 1))</math>		\|<math>(\lambda 1 1 (\lambda 1 (\lambda\lambda\lambda\lambda 1 4 4 4 3 2 1) 1 1 1 1) 1) (\lambda\lambda 2 (2 1))</math>
	\|-		\|-
	\|BBλ(~~213~~)		\|BBλ(201)
	\|> q(5)		\|> q(5)
	\|<code>too large to show</code>		\|<code>too large to show</code>

Polygon: /* Oracle Busy Beaver for Lambda Calculus (BBλ1(n)) */ changed formatting

2026-02-14T08:59:05Z

Oracle Busy Beaver for Lambda Calculus (BBλ1(n)): changed formatting

← Older revision		Revision as of 08:59, 14 February 2026
Line 1,188:		Line 1,188:
	\|BBλ<sub>1</sub>(2)		\|BBλ<sub>1</sub>(2)
	\|1		\|1
	\|<~~code~~>1</~~code~~>		\|<math>1</math>
	\|-		\|-
	\|BBλ<sub>1</sub>(3)		\|BBλ<sub>1</sub>(3)
Line 1,196:		Line 1,196:
	\|BBλ<sub>1</sub>(4)		\|BBλ<sub>1</sub>(4)
	\|4		\|4
	\|<~~code~~>\1</~~code~~>		\|<math>\lambda 1</math>
	\|-		\|-
	\|BBλ<sub>1</sub>(5)		\|BBλ<sub>1</sub>(5)
	\|5		\|5
	\|<~~code~~>\2</~~code~~>		\|<math>\lambda 2</math>
	\|-		\|-
	\|BBλ<sub>1</sub>(6)		\|BBλ<sub>1</sub>(6)
	\|6		\|6
	\|<~~code~~>\\1</~~code~~>		\|<math>\lambda \lambda 1</math>
	\|-		\|-
	\|BBλ<sub>1</sub>(7)		\|BBλ<sub>1</sub>(7)
	\|7		\|7
	\|<~~code~~>\\2</~~code~~>		\|<math>\lambda \lambda 2</math>
	\|-		\|-
	\|BBλ<sub>1</sub>(8)		\|BBλ<sub>1</sub>(8)
	\|26		\|26
	\|<~~code~~>1 (\1)</~~code~~>		\|<math>1 (\lambda 1)</math>
	\|-		\|-
	\|BBλ<sub>1</sub>(9)		\|BBλ<sub>1</sub>(9)
	\|9		\|9
	\|<~~code~~>\\2</~~code~~>		\|<math>\lambda \lambda 2</math>
	\|-		\|-
	\|BBλ<sub>1</sub>(10)		\|BBλ<sub>1</sub>(10)
	\|36		\|36
	\|<~~code~~>1 (\\1)</~~code~~>		\|<math>1 (\lambda \lambda 1)</math>
	\|-		\|-
	\|BBλ<sub>1</sub>(11)		\|BBλ<sub>1</sub>(11)
	\|41		\|41
	\|<~~code~~>1 (\\2)</~~code~~>		\|<math>1 (\lambda \lambda 2)</math>
	\|-		\|-
	\|BBλ<sub>1</sub>(12)		\|BBλ<sub>1</sub>(12)
	\|266		\|266
	\|<~~code~~>1 (1 (\1))</~~code~~>		\|<math>1 (1 (\lambda 1))</math>
	\|-		\|-
	\|BBλ<sub>1</sub>(13)		\|BBλ<sub>1</sub>(13)
	\|51		\|51
	\|<~~code~~>1 (\\2)</~~code~~>		\|<math>1 (\lambda \lambda 2)</math>
	\|-		\|-
	\|BBλ<sub>1</sub>(14)		\|BBλ<sub>1</sub>(14)
	\|<math>f(36) = 25 \times 2^{2^{2^{3}}}+36 > 2.85 \times 10^{78}</math>		\|<math>f(36) = 25 \times 2^{2^{2^{3}}}+36 > 2.85 \times 10^{78}</math>
	\|<~~code~~>1 (1 (\\1))</~~code~~>		\|<math>1 (1 (\lambda \lambda 1))</math>
	\|-		\|-
	\|BBλ<sub>1</sub>(15)		\|BBλ<sub>1</sub>(15)
	\|<math>f(41) \geq 25 \times 3^{3^{85}}+36 > 10^{1.7 \times 10^{40}}</math>		\|<math>f(41) \geq 25 \times 3^{3^{85}}+36 > 10^{1.7 \times 10^{40}}</math>
	\|<~~code~~>1 (1 (\\2))</~~code~~>		\|<math>1 (1 (\lambda \lambda 2))</math>
	\|-		\|-
	\|BBλ<sub>1</sub>(16)		\|BBλ<sub>1</sub>(16)
	\|<math>f(266)</math>		\|<math>f(266)</math>
	\|<~~code~~>1 (1 (1 (\1)))</~~code~~>		\|<math>1 (1 (1 (\lambda 1)))</math>
	\|-		\|-
	\|BBλ<sub>1</sub>(17)		\|BBλ<sub>1</sub>(17)
	\|<math>f(51)</math>		\|<math>f(51)</math>
	\|<~~code~~>1 (1 (\\\2))</~~code~~>		\|<math>1 (1 (\lambda \lambda \lambda 2))</math>
	\|-		\|-
	\|BBλ<sub>1</sub>(18)		\|BBλ<sub>1</sub>(18)
	\|<math>f^{4}(4) = f(f(266))</math>		\|<math>f^{4}(4) = f(f(266))</math>
	\|<~~code~~>1 (\1) 1 (\1)</~~code~~>		\|<math>1 (\lambda 1) 1 (\lambda 1)</math>
	\|-		\|-
	\|BBλ<sub>1</sub>(19)		\|BBλ<sub>1</sub>(19)
	\|<math>f^{3}(7) = f(f(41))</math>		\|<math>f^{3}(7) = f(f(41))</math>
	\|<~~code~~>1 (1 (1 (\\2)))</~~code~~>		\|<math>1 (1 (1 (\lambda \lambda 2)))</math>
	\|-		\|-
	\|BBλ<sub>1</sub>(20)		\|BBλ<sub>1</sub>(20)
	\|<math>f^{6}(4) = f^{4}(266)</math>		\|<math>f^{6}(4) = f^{4}(266)</math>
	\|<~~code~~>1 (\\1) 1 (\1)</~~code~~>		\|<math>1 (\lambda \lambda 1) 1 (\lambda 1)</math>
	\|-		\|-
	\|BBλ<sub>1</sub>(21)		\|BBλ<sub>1</sub>(21)
	\|<math>f^{7}(4) = f^{5}(266)</math>		\|<math>f^{7}(4) = f^{5}(266)</math>
	\|<~~code~~>1 (\\2) 1 (\1)</~~code~~>		\|<math>1 (\lambda \lambda 2) 1 (\lambda 1)</math>
	\|-		\|-
	\|BBλ<sub>1</sub>(22)		\|BBλ<sub>1</sub>(22)
	\|<math>f^{52}(4) = f^{50}(266)</math>		\|<math>f^{52}(4) = f^{50}(266)</math>
	\|<~~code~~>1 (1(\1)) 1(\1)</~~code~~>		\|<math>1 (1 (\lambda 1)) 1 (\lambda 1)</math>
	\|-		\|-
	\|BBλ<sub>1</sub>(28)		\|BBλ<sub>1</sub>(28)
	\|<math>\geq f^{BB \lambda(f^{3}(4))}(4)</math>		\|<math>\geq f^{BB \lambda(f^{3}(4))}(4)</math>
	\|<~~code~~>1 (\1) 1 (\1) 1 (\1)</~~code~~>		\|<math>1 (\lambda 1) 1 (\lambda 1) 1 (\lambda 1)</math>
	\|-		\|-
	\|BBλ<sub>1</sub>(29)		\|BBλ<sub>1</sub>(29)
	\|<math>\geq f^{BB \lambda(f^{BB \lambda(f^{4}(4))+4}(4))+BB \lambda(f^{4}(4))+5}(4)</math>		\|<math>\geq f^{BB \lambda(f^{BB \lambda(f^{4}(4))+4}(4))+BB \lambda(f^{4}(4))+5}(4)</math>
	\|<~~code~~>1(\1)(\1 2 1)(\1)</~~code~~>		\|<math>1(\lambda 1)(\lambda 1 2 1)(\lambda 1)</math>
	\|}		\|}

Polygon: /* Regular Busy Beaver for Lambda Calculus (BBλ(n)) */ updated list

2026-02-14T08:49:27Z

Regular Busy Beaver for Lambda Calculus (BBλ(n)): updated list

Show changes

Polygon: /* Busy Beaver for De Bruijn Lambda Calculus */ updated champions

2026-02-06T17:48:06Z

Busy Beaver for De Bruijn Lambda Calculus: updated champions

← Older revision		Revision as of 17:48, 6 February 2026
Line 1,250:		Line 1,250:
	\|-		\|-
	\|18		\|18
	\|<math>f_{\omega^3}(2)</math>		\|<math>> f_{\omega^\omega}(2 \uparrow\uparrow 18)</math>
	\|<code>(\1 1 (\\\1 3 2 1) 1 1 1) (\\2 (2 1))</code>		\|<code>(\1 1 1) (\1 (1 (\\\1 3 2 (\\2 (2 1)))))</code>
			\|-
			\|22
			\|<math>> f_{\omega^{\omega+2}}(2)</math>
			\|<code>(\1 (\\\\1 4 4 4 3 2 1) 1 1 1 1) (\\2 (2 1))</code>
			\|-
			\|23
			\|<math>> f_{\zeta_0}(15)</math>
			\|<code>(\1 1 (\\\\1 4 4 4 3 2 1) 1 1 1 1) (\\2 (2 1))</code>
			\|-
			\|24
			\|<math>> f_{\psi(\Omega_\omega)}(12)</math>
			\|<code>(\1 1 1 (\\\\1 4 4 4 3 2 1) 1 1 1 1) (\\2 (2 1))</code>
			\|-
			\|25
			\|<math>> f_{\psi(\Omega_\omega)}(f_{\omega^{\omega+2}}(2))</math>
			\|<code>(\1 (\1 (\\\\1 4 4 4 3 2 1) 1 1 1 1) 1) (\\2 (2 1))</code>
	\|-		\|-
	\|26		\|26
	\|<math>f_{\~~epsilon_0~~+1}(3)</math>		\|<math>> f_{\psi(\Omega_\omega+1)}(4)</math>
	\|<code>(\1 1 (\1 1) (\\1 2 1) (\1 ~~(\2~~ 1 2))) (\\\2 3 (\3 1 2))</code>		\|<code>(\1 1 (\1 (\\\\1 4 4 4 3 2 1) 1 1 1 1) 1) (\\2 (2 1))</code>
	\|}		\|}

Polygon: /* Regular Busy Beaver for Lambda Calculus (BBλ(n)) */ added new champions

2026-02-06T17:45:26Z

Regular Busy Beaver for Lambda Calculus (BBλ(n)): added new champions

← Older revision		Revision as of 17:45, 6 February 2026
Line 1,069:		Line 1,069:
	\|<code>(\1 1) (\1 (1 (\\1 2 (\\2 (2 1)))))</code>		\|<code>(\1 1) (\1 (1 (\\1 2 (\\2 (2 1)))))</code>
	\|-		\|-
	\|BBλ(63)		\|BBλ(61)
	\|<math>> f_{\omega^3}\left(2\right)</math>		\|<math>> f_{\omega^{2 \uparrow\uparrow 18-1}}\left(2\right)</math>
	\|<code>(\1 1 (\\\1 3 2 ~~1) 1 1 1)~~ (\\2 (2 1))</code>		\|<code>(\1 1 1) (\1 (1 (\\\1 3 2 (\\2 (2 1)))))</code>
	\|-		\|-
	\|BBλ(91)		\|BBλ(86)
	\|<math>> f_{~~\varepsilon_0~~ \omega^{\omega^{3}}}\left(4\right)</math>		\|<math>> f_{\omega^{\omega^{2}}}\left(2\right)</math>
	\|<code>(\1 1 (\1 1) (\\1 2 1) (\1 (\2 1 2))) (\\\2 3 (\3 1 2))</code>		\|<code>(\1 (\\\\1 4 4 4 3 2 1) 1 1 1 1) (\\2 (2 1))</code>
			\|-
			\|BBλ(90)
			\|<math>> f_{\zeta_0}\left(15\right)</math>
			\|<code>(\1 1 (\\\\1 4 4 4 3 2 1) 1 1 1 1) (\\2 (2 1))</code>
			\|-
			\|BBλ(94)
			\|<math>> f_{\psi(\Omega_\omega)}\left(12\right)</math>
			\|<code>(\1 1 1 (\\\\1 4 4 4 3 2 1) 1 1 1 1) (\\2 (2 1))</code>
			\|-
			\|BBλ(96)
			\|<math>> f_{\psi(\Omega_\omega)}\left(f_{\omega^{\omega^{2}}}\left(2\right)\right)</math>
			\|<code>(\1 (\1 (\\\\1 4 4 4 3 2 1) 1 1 1 1) 1) (\\2 (2 1))</code>
			\|-
			\|BBλ(100)
			\|<math>> f_{\psi(\Omega_\omega)+1}\left(4\right)</math>
			\|<code>(\1 1 (\1 (\\\\1 4 4 4 3 2 1) 1 1 1 1) 1) (\\2 (2 1))</code>
			\|-
			\|BBλ(331)
			\| lim(BMS)
			\|<code>too large to show</code>
	\|-		\|-
	\|BBλ(1850)		\|BBλ(1850)