\begin{definition}[Definition:Fermat Number/Naming Conventions]
The '''Fermat number''' $F_0$ is often referred to as the ''' $1$st Fermat number''', so (confusingly) this convention dictates that $F_n$ is the '''$n + 1$th Fermat number'''.
However, another convention is that $F_0$ can be referred to as the '''zeroth Fermat number''', thus bringing the appellation in line such that $F_n$ is the '''$n$th Fermat number'''.
Both conventions are in place, sometimes in the same work.
For example, {{AuthorRef|David Wells}}, in his {{BookLink|Curious and Interesting Numbers|David Wells|ed = 2nd|edpage = Second Edition}} of $1997$, refers to $5 = F_1$ in Section $5$ as the '''$2$nd Fermat number'''.
However, in Section $257$ he defines $F_3 = 2^{2^3} + 1 = 257$ as the '''$3$rd Fermat number'''.
Similarly, in Section $65,537$ he defines $F_4 = 2^{2^4} + 1 = 65 \, 537$ as the '''$4$th Fermat number''', and so on.
Both of these naming conventions is more or less clumsy.
{{ProofWiki}} takes the position that the cat has to jump one way or the other, and so uses the second of these conventions:
:$F_n$ is the '''$n$th Fermat number'''.
Category:Definitions/Fermat Numbers
\end{definition}