The Busy Beaver Competitions
with: Current Records, Winning Turing Machines, References
Created by Pascal Michel in 2004
Last update: September 2024
If you do not understand the following definitions,
you need elementary stuff on Turing machines and Busy Beavers.
Definitions
S(k,n) is the maximum number of steps made by a Turing machine with k states and n symbols that stops when starting from a blank tape.
Sigma(k,n) is the maximum number of nonblank symbols left on the tape by such a machine.
Records for the Busy Beaver Competitions
Only the current records are given here.
The previous records are given in the historical survey of the busy beaver competition.
Machines with 2 symbols
Machines with 3 symbols
Machines with 4 symbols
Machines with 5 symbols
Machines with 6 symbols
Summary tables
For S(k,n):
6 symbols  > 10^^(10^^10^{10115})  
5 symbols  > 10^(10^(10^3,314,360))  ?  
4 symbols  3,932,964  > 2(^^{15})5 + 14  ?  
3 symbols  38  > 1.1 × 10^{17}  > 1.0 × 10^{14072}  ?  
2 symbols  6  21  107  47,176,870  > 10^^15 
2 states  3 states  4 states  5 states  6 states 
For Sigma(k,n):
6 symbols  > 10^^(10^^10^{10115})  
5 symbols  > 10^(10^(10^3,314,360))  ?  
4 symbols  2,050  2(^^{15})5 + 14 ?  ?  
3 symbols  9  374,676,383 ?  > 1.3 × 10^{7036}  ?  
2 symbols  4  6  13  4098  > 10^^15 
2 states  3 states  4 states  5 states  6 states 
Winning machines
Other good machines are given in the historical survey.
Turing machines with 2 states and 2 symbols

M= 

Turing machines with 3 states and 2 symbols

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M= 

Turing machines with 4 states and 2 symbols

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Turing machines with 5 states and 2 symbols

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Turing machines with 6 states and 2 symbols

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Turing machines with 7 states and 2 symbols

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Turing machines with 2 states and 3 symbols

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Turing machines with 3 states and 3 symbols

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Turing machines with 4 states and 3 symbols

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Turing machines with 2 states and 4 symbols

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Turing machines with 3 states and 4 symbols

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Turing machines with 2 states and 5 symbols



Turing machines with 2 states and 6 symbols



References