>In order to generate e, we'll need to find a random prime number that has a greatest common divisor (GCD) of 1 in relation to ϕ(n).

How can a prime number have any divisor that isn't 1, let alone a gcd? Either that's mistaken, or it's unnecessary to state.

A prime is a divisor of itself. What it is in effect saying is "find a random prime number that is not a divisor of ϕ(n)".

I'm not sure why it is saying that, though, because RSA does not require e to be a prime number. It just requires that gcd(e,ϕ(n)) = 1.

The article is just poorly written, as can be seen by this sentence a little further down:

> The e value is often made up; it's an arbitrary factor of both of your primes.

I cannot even begin to figure out where that came from.