I'm currently writing a paper about RSA (a self-chosen subject). I'm writing about the key-generation in RSA, and I have problem finding the public exponent e.
I have chosen p = 61 and q = 53.
Then I determined my modulus n = p ⋅ q = 3233
and my phi(n) = (p-1)(q-1) = 3120.
What bothers me is that when I try to generate the public exponent e using CrypTool (given the same parameters), it gives me e = 2^16+1 = 65537 BUT I thought e had to be less that phi(n) = (p-1)(q-1) (according to this source). Why is it OK to break this rule? Or is the CrypTool faulty?