Such numbers are best understood in terms of some computability
hierarchy. A common starting point is Ackermann's function, a
version of which grows faster than any primitive recursive
function (i.e. any fortran function definable with for loops,
successor, and unlimited resources) . I will let you look up the
function so that I do not misstate its definition. A(4,4) is
something like the number of quarks in the universe, A(5,5) the
number of arrangements of such quarks, and Graham's number is
something like A(6,6). (I am making these up. Check elsewhere
for the actual numbers. The above is just to give you an idea of
scale.) EDIT: Another poster has fixed the idea of scale,
showing that Graham's number is much larger than I represent
above. That poster also goes on to mention n(4) from the article
mentioned below is in turn much larger than Graham's number
which is much larger than n(3). However, Graham's number is near
the beginning of a list of enormous numbers. Harvey Friedman has
a paper on some nice com