In Apostol's "Introduction to Analytic Number Theory" on page 7 he introduces Fermat numbers of the form $F_n = 2^{2^{n}} + 1$ where $n$ is a non-negative integer. He then states that
The greatest known Fermat composite, $F_{1945}$, has more than $10^{582}$ digits, a number larger than the number of letters in the Los Angeles and New York telephone directories combined.
This is a true statement, but unless I'm misinterpreting the phone book estimate, it falls quite a bit short of capturing the enormity of $2^{2^{1945}}$, which is more than the number of atoms in multiple universes.
The way I am interpreting the phone book estimate is that one counts the number of letters and numbers in the phone book and multiplies them by the population of NY and LA.
Is there a different way to interpret this statement so that it is closer to the value of $F_{1945}$?