Today we were discussing in our class about usefulness of a number no problem how large,small may be it's value. As per my knowledge (till grade 11) Avogadro number $N_A=6.022\times 10^{23}$ is a very useful number while G=$6.67\times 10^{-11}$ is small but useful in physics. But I don't know if there exists a number far larger than what I mentioned but used in real life. Note $\infty$ isn't of my interest .
2026-03-25 17:18:23.1774459103
Large, small but a useful number.
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Wikipedia has a few here.
Here is Graham himself explaining what Graham's number expresses. (It's an upper bound for an geometric problem).
It has been constructed to make a proof work so it's not a arbitrary construct. However I'm not sure if you would still consider this as "used in real life".
It's large enough that you can't express it in a regular notation.