Lunillion

The lunillion is equal to $$10^{3 \cdot 10^{3 \cdot 10^{3\text{ quadrillion}}} + 3}$$, or $$10^{3 \cdot 10^{3 \cdot 10^{3 \cdot 10^{15}}} + 3}$$. The term was coined by Jonathan Bowers.

Etymology
The name of this number is based on the word "Lun a" (Latin for "moon") and the suffix "-illion".