Definition:Euclid Number/Historical Note

Historical Note on Euclid Number
The name Euclid number derives from 's proof of the Infinitude of Prime Numbers.

It is often stated (erroneously) that this proof relies on these numbers.

However, recall that did not begin by assuming that the set of all primes is finite. His proof, found in as, 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, they have been (however mistakenly) named after him.