Golden Prime Symmetry

The new theorems of Golden Prime Symmetry proves geometrically the existence of an equivalence relation on the infinite set of prime numbers. The golden ratio it induces a partition into 8 equivalence classes corresponding to 8 rotation invariant angles or isometries of 2 opposite pentagons rotated in the complex plane. Moreover, when arranged in matrices they form a Lie rotation group. The quotient set of residual prime classes corresponds to the zeros of a minimal irreducible polynomial over Q corresponding to a cyclotomic polynomial of order 5. Analogously, there is another equivalence relation on the infinite set of the twelfth Fibonacci numbers which has the same properties for two other opposite pentagons rotated in the complex plane. Thus, it is shown that the sine function maps the prime numbers into unique golden images that depend on the last digit of the prime (1, 3, 7, 9).