Supillion

The supillion is equal to $$10^{3 \cdot 10^{3 \cdot 10^{3 \cdot \text{undecillion}}} + 3}$$, or $$10^{3 \cdot 10^{3 \cdot 10^{3 \cdot 10^{36}}} + 3}$$. The term was coined by Jonathan Bowers.

Etymology
The name of this number is based on the phrase "Sup ercluster" and the suffix "-illion".