Is any property of the number TREE($3$) known? The number TREE($3$) is an insane large number occuring in Ramsey theory.

For the usual large numbers constructed with Knut's up-arrow-notation, Conway chain-notation and Bowers array-notation, it is usually easy to determine the last few digits of the constructed number because mostly power towers with many identical entries come into play.


  Is that also the case for TREE($3$) ? I have read that no upper bound is known, but it might be that the number is known to be a huge power tower. So, can we determine the last digits of TREE($3$) ? Or do we know nothing, not even whether TREE($3$) is even or odd ?
Yes, I have used the last binary (NOT decimal) digits of the tree steps and proven that it is odd and the last 3 binary digits are 011.
Yes, I have used the last binary (NOT decimal) digits of the tree steps and proven that it is odd and the last 3 binary digits are 011.