Could Graham's number be stored in a modern computer?

Theoretically, enough of the formula behind it could be stored so that pieces of it could be calculated. For example, if you just wanted to look at the last ten digits or something like that. However, the entire number is far to big to be stored in perfect precision by any computer that has ever existed or ever will exist. How can I say "ever will exist"? Because, even written in scientific notation, i.e. with only one digit of precision, the number of digits in the exponent would exceed the number of atoms in the observable universe. The total number is easily larger than the number of Planck volumes into which the observable universe can be divided. If the whole observable universe were a computer, and every tiny quark and neutrino represented a bit of data, it could not store the entire number in absolute precision. And better observational equipment would not help expand the observable universe into a larger computer, since, at this level, the observable universe is bound not so much by our technology, but rather by the speed of light itself. So, the short answer to your question is "No."