The last entry in
The Penguin Dictionary of Curious and Interesting
by David Wells:
The World Champion largest number, listed in the last
Guinness Book of Records
is an upper bound, derived by R. L. Graham, from a problem in a part of
combinatorics called Ramsey theory.
Graham's number cannot be expressed using the conventional notation of
powers, and powers of powers. If all the material in the universe were turned into
pen and ink it would not be enough to write the number down. Consequently,
this special notation, devised by Donald Knuth is necessary.
Guiness Book of World Record, 1980
Page 193, line 27-31