In this paper, the unpublished mathematical relation discovered by the author, about the existence of an equivalence relation on the infinite set of prime numbers, is demonstrated. That is, the golden ratio (1 + √ 5)/2 orders and classifies all prime numbers p > 5 into 8 infinite families according to their last and penultimate digit. That is, it induces a partition into 8 equivalence prime classes by 8 rational angles that are invariant under rotations of the regular pentagon in the complex plane. The prime classes in the complex plane correspond to the zeros of the cyclotomic polynomial number 20. Analogously, there is another equivalence relation on the infinite set of the twelfth Fibonacci numbers F_12(5m+j) , which has the same properties in the complex plane.