The bound on BB(6) has grown from 10^36,534 to an iterated exponentiation tower of height 15 with base 10.
Mxdys improved the bound to an iterated exponentiation tower of ten million 10s, with a Coq-verified proof.
A further update shows BB(6) is at least 2 tetrated three levels deep ending in 9, equivalent to 2 pentated to 5.
These findings illustrate the jump from BB(5)=47 million to BB(6) far beyond any observable or conventional large numbers.
The new enormity of BB(6) suggests the Busy Beaver function may become independent of ZFC axioms at a much lower n than previously thought.
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