Gaxillion

The gaxillion is equal to $$10^{3 \cdot 10^{3 \cdot 10^{3 \cdot \text{decillion}}} + 3}$$, or $$10^{3 \cdot 10^{3 \cdot 10^{3 \cdot 10^{33}}} + 3}$$.

Etymology
The name of this number is based on the word "Ga lax y" and the suffix "-illion".