lg(lg(N)) is very small, for 1e30, the value is
approximately ~6 and at 1e60 it is ~7.6, at which point lg(lg(N)) is pretty much a constant value (or trivial), but yes - it is technically included in the growth rate, but for practical purposes can probably be ignored
The list of big O classes is the following:
lg(lg(N)) is very small, for 1e30, the value is approximately ~6 and at 1e60 it is ~7.6, at which point lg(lg(N)) is pretty much a constant value (or trivial), but yes - it is technically included in the growth rate, but for practical purposes can probably be ignored