<p>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).</p>

Golden Prime Symmetry establishes the algebraic and geometric relationship between prime numbers and the golden ratio. 

Organisation	Role	Department	Start date	End date
University of Tolima	Not specified	Not specified
University of Tolima	Mathematician	Not specified	2016-06-06

Organisation	Degree/title	Department	Start date	End date
University of Tolima	Not specified	Not specified
University of Tolima	Mathematician	Not specified	2016-06-06

Javier Grisales Herrera

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