BB(2,6): Difference between revisions

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The 2-state, 6-symbol Busy Beaver problem, '''BB(2,6),''' is unsolved. With cryptids like [[Hydra]] in the preceding domain [[BB(2,5)]], we know that we must solve a [[Collatz-like]] problem in order to solve BB(2,6).
The 2-state, 6-symbol Busy Beaver problem, '''BB(2,6),''' is unsolved. With cryptids like [[Hydra]] in the preceding domain [[BB(2,5)]], we know that we must solve a [[Collatz-like]] problem in order to solve BB(2,6).


The current BB(2,6) champion {{TM|1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA|halting}} was discovered by Pavel Kropitz in May 2023, proving the lower bound:<math display="block">S(2,6) > \Sigma(2,6) > 10 \uparrow \uparrow 10 \uparrow\uparrow 10^{10^{115}} > 10 \uparrow \uparrow \uparrow 3</math>
The current BB(2,6) champion {{TM|1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA|halt}} was discovered by Pavel Kropitz in May 2023, proving the lower bound:<math display="block">S(2,6) > \Sigma(2,6) > 10 \uparrow \uparrow 10 \uparrow\uparrow 10^{10^{115}} > 10 \uparrow \uparrow \uparrow 3</math>


== Top Halters ==
== Top Halters ==
Line 11: Line 11:
!Discoverer
!Discoverer
|-
|-
|{{TM|1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA|halting}}
|{{TM|1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA|halt}}
|10 ↑↑↑ 3
|10 ↑↑↑ 3
|Pavel Kropitz
|Pavel Kropitz
|-
|-
|{{TM|1RB3LA4LB0RB1RA3LA_2LA2RA4LA1RA5RB1RZ|halting}}
|{{TM|1RB3LA4LB0RB1RA3LA_2LA2RA4LA1RA5RB1RZ|halt}}
|10 ↑↑ 91  
|10 ↑↑ 91  
|Pavel Kropitz
|Pavel Kropitz
|-
|-
|{{TM|1RB2LA1RA4LA5RA0LB_1LA3RA2RB1RZ3RB4LA|halting}}
|{{TM|1RB2LA1RA4LA5RA0LB_1LA3RA2RB1RZ3RB4LA|halt}}
|10 ↑↑ 70  
|10 ↑↑ 70  
|Shawn Ligocki
|Shawn Ligocki
|-
|-
|{{TM|1RB2LB0RA2RA5RA1LB_2LA4RB3LB2RB0RB1RZ|halting}}
|{{TM|1RB2LB0RA2RA5RA1LB_2LA4RB3LB2RB0RB1RZ|halt}}
|10 ↑↑ 54.90  
|10 ↑↑ 54.90  
|Andrew Ducharme*
|Andrew Ducharme*
|-
|-
|{{TM|1RB3RB1LB5LA2LB1RZ_2LA3RA4RB2LB0LA4RB|halting}}
|{{TM|1RB3RB1LB5LA2LB1RZ_2LA3RA4RB2LB0LA4RB|halt}}
|10 ↑↑ 42.17  
|10 ↑↑ 42.17  
|Andrew Ducharme*
|Andrew Ducharme*
|-
|-
|{{TM|1RB3LB0RB5RA1LB1RZ_2LB3LA4RA0RB0RA2LB|halting}}
|{{TM|1RB3LB0RB5RA1LB1RZ_2LB3LA4RA0RB0RA2LB|halt}}
|10 ↑↑ 40.07
|10 ↑↑ 40.07
|Andrew Ducharme*
|Andrew Ducharme*
|-
|-
|{{TM|1RB3LB3RB4LA2LA4LA_2LA2RB1LB0RA5RA1RZ|halting}}
|{{TM|1RB3LB3RB4LA2LA4LA_2LA2RB1LB0RA5RA1RZ|halt}}
|10 ↑↑ 21.54
|10 ↑↑ 21.54
|Andrew Ducharme*
|Andrew Ducharme*
|-
|-
|{{TM|1RB0RA3RB0LB1RA2LA_2LA4LB1RA3LB5LB1RZ|halting}}
|{{TM|1RB0RA3RB0LB1RA2LA_2LA4LB1RA3LB5LB1RZ|halt}}
|10 ↑↑ 17.53
|10 ↑↑ 17.53
|Andrew Ducharme*
|Andrew Ducharme*
|-
|-
|{{TM|1RB0RA3RB0LB5LA2LA_2LA4LB1RA3LB5LB1RZ|halting}}
|{{TM|1RB0RA3RB0LB5LA2LA_2LA4LB1RA3LB5LB1RZ|halt}}
|10 ↑↑ 17.53
|10 ↑↑ 17.53
|Andrew Ducharme*
|Andrew Ducharme*
|-
|-
|{{TM|1RB3RA4LA1LA0LA1RZ_2LA0LB1RA1LB5LB2RA|halting}}
|{{TM|1RB3RA4LA1LA0LA1RZ_2LA0LB1RA1LB5LB2RA|halt}}
|10 ↑↑ 15.49
|10 ↑↑ 15.49
|Andrew Ducharme*
|Andrew Ducharme*
|}
|}
All decimal places are truncated. Discoverers are asterisked where it is unclear if the TM had been found but unreported by someone previously (namely Shawn Ligocki).
All decimal places are truncated. Discoverers are asterisked where it is unclear if the TM had been found but unreported by someone previously (namely Shawn Ligocki).
[[Category: BB Domains]]

Latest revision as of 20:01, 25 August 2025

The 2-state, 6-symbol Busy Beaver problem, BB(2,6), is unsolved. With cryptids like Hydra in the preceding domain BB(2,5), we know that we must solve a Collatz-like problem in order to solve BB(2,6).

The current BB(2,6) champion 1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA (bbch) was discovered by Pavel Kropitz in May 2023, proving the lower bound:

Top Halters

The highest known scoring machines are:

TM Approximate sigma score Discoverer
1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA (bbch) 10 ↑↑↑ 3 Pavel Kropitz
1RB3LA4LB0RB1RA3LA_2LA2RA4LA1RA5RB1RZ (bbch) 10 ↑↑ 91 Pavel Kropitz
1RB2LA1RA4LA5RA0LB_1LA3RA2RB1RZ3RB4LA (bbch) 10 ↑↑ 70 Shawn Ligocki
1RB2LB0RA2RA5RA1LB_2LA4RB3LB2RB0RB1RZ (bbch) 10 ↑↑ 54.90 Andrew Ducharme*
1RB3RB1LB5LA2LB1RZ_2LA3RA4RB2LB0LA4RB (bbch) 10 ↑↑ 42.17 Andrew Ducharme*
1RB3LB0RB5RA1LB1RZ_2LB3LA4RA0RB0RA2LB (bbch) 10 ↑↑ 40.07 Andrew Ducharme*
1RB3LB3RB4LA2LA4LA_2LA2RB1LB0RA5RA1RZ (bbch) 10 ↑↑ 21.54 Andrew Ducharme*
1RB0RA3RB0LB1RA2LA_2LA4LB1RA3LB5LB1RZ (bbch) 10 ↑↑ 17.53 Andrew Ducharme*
1RB0RA3RB0LB5LA2LA_2LA4LB1RA3LB5LB1RZ (bbch) 10 ↑↑ 17.53 Andrew Ducharme*
1RB3RA4LA1LA0LA1RZ_2LA0LB1RA1LB5LB2RA (bbch) 10 ↑↑ 15.49 Andrew Ducharme*

All decimal places are truncated. Discoverers are asterisked where it is unclear if the TM had been found but unreported by someone previously (namely Shawn Ligocki).

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