Busy beaver ones function $\Sigma(6)$
The maximum number of 1s left on the tape by a $6$-state, 2-symbol Turing machine that halts when started on a blank tape.
Lower bound:
$2\uparrow\uparrow 2\uparrow\uparrow 2\uparrow\uparrow 10$
Upper bound:
Unknown
Updates from the literature
-
2011
Lower bound: $3.5\times10^{18267}$
Kropitz, P. (2011). Problém busy beaver.
[via The Busy Beaver Frontier, Scott Aaronson, 2020-09-29] -
2022-05
Lower bound: $10\uparrow\uparrow 15$
Pavel Kropitz in May 2022
[via The Busy Beaver Competition: a historical survey, Pascal Michel] -
2025-06
Lower bound: $2\uparrow\uparrow 2\uparrow\uparrow 2\uparrow\uparrow 10$
mxdys in June 2025
[via The Busy Beaver Competition: a historical survey, Pascal Michel]