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 ==
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!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*

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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