Busy Beaver ones function value $\Sigma(7)$
The maximal number of 1s that a $7$-state Turing machine can print on an initially blank tape before eventually halting.
Lower bound:
$10^{10^{10^{10^{18705353}}}}$
Upper bound:
Unknown
Updates
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Lower bound: $10^{10^{10^{10^{18705353}}}}$
Reference unknown
[via The Busy Beaver Frontier, Scott Aaronson, 2020-09-29]