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Numbers above about 10184 are of dubious utility, since that's the approximate volume of the observable universe in cubic Planck lengths 🙂
If you were to write Graham’s number out digit by digit (for example, one hundred =100), putting a digit in each cubic Planck length of the known universe (a Planck length being the smallest measurement science has), you’d have no where near enough space to write out the entire number.
I find it inspiring that the human mind is capable of (at least kind of) conceptualising and expressing an exact number that is so large that it can’t fit in the physical universe.
The arrows you mean? https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation
For most people it comes under the realm of "maths trivia" because it's never practically useful. You wouldn't have seen it before unless you hang around with maths nerds or read about maths for fun. So I wouldn't feel stupid if I were you.
Graham's number is a fucking massive number that is an upper bound/maximum on the answer to some question about colouring.