A proof technique perhaps altogether new to mathematical logic. I draw an example from biology to make the mathematical logic more readily visible.
Infinity always hurts the brain when trying to solve a problem which deals with infinity.
Infinity is counterintuitive, anyone can refer to many various works on infinite sets and realize how puzzling and how terribly difficult infinity is. This proof is difficult to intuitively see, thus it is the most difficult to hold in the mind for any long period of time. Construct long sequences of consecutive numbers that are not prime. Using the theorem that between M and 2M, there has to exist at least one prime number. The set of primes are infinite.