Busy Beaver number $BB(7)$
The maximal number of steps that a $7$-state Turing machine can make on an initially blank tape before eventually halting.
Lower bound:
$10^{2\times10^{10^{10^{18705353}}}}$
Upper bound:
Unknown
Updates
-
Lower bound: $10^{2\times10^{10^{10^{18705353}}}}$
Reference unknown
[via The Busy Beaver Frontier, Scott Aaronson, 2020-09-29]