In practice, it's very common to set e, e equal to 3.
Or e equal to two to the 16 plus 1.
And the reason for that is to allow efficient exponentiation.
So think about e equals 3 in particular e equals 3 is a small number.
And therefore raising to the eth power is very efficient, can be done very quickly.
Similarly, e equals 2 the 16 plus 1 if you think about the way
that's written in binary.
2 the 16 plus one will be an integer with exactly two ones and the rest zeros.
And if you think about also the way we defined our exponentiation algorithm,
this will also lead to an efficient way an efficient algorithm for
raising things to the eth power.
So if you do things this way,
you just have to be a little bit careful to choose p and q in such a way that phi
of N will be relatively prime to one of these values of e.