Betillion

The betillion is equal to $$10^{3 \cdot 10^{3 \cdot 10^{3 \cdot \text{octillion}}} + 3}$$, or $$10^{3 \cdot 10^{3 \cdot 10^{3 \cdot 10^{27}}} + 3}$$. Trakaplex has got the prefix "beta-" out of it.

Etymology
The name of this number is based on the word "Bet elgeuse" and the suffix "-illion".