\begin{definition}[Definition:Euclid Number/Historical Note]
The name '''Euclid number''' derives (erroneously) from Euclid's Theorem: {{AuthorRef|Euclid}}'s proof of the Infinitude of Prime Numbers. It is often said that this proof relies on these numbers.
However, recall that {{AuthorRef|Euclid}} did not begin by assuming that the set of all primes is finite. His proof, found in {{ElementsLink}} as {{EuclidPropLink|book = IX|prop = 20|title = Euclid's Theorem}}, proceeded as follows:
:Take any finite set of primes (it could be any set, for example $\left\{ {3, 211, 65537}\right\}$). Then it follows that at least one prime exists that is not in that set.
However, the numbers themselves are mildly interesting in their own right.
Hence, in honour of {{AuthorRef|Euclid}}, they have been (however mistakenly) named after him.
Category:Historical Notes
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Prime.mover
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\end{definition}