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).
Golden Prime Symmetry
Publication type:Research Problem
Published:
Language:English
Licence:
CC BY 4.0
DOI (This Version):
https://doi.org/10.57874/ahv3-ap89
DOI (All Versions):
https://doi.org/10.57874/ctxe-h181
Peer Reviews (This Version): (0)
Red flags:
(0)
Actions
Download:
Sign in for more actionsSections
Research topics above this in the hierarchy
Funders
No sources of funding have been specified for this Research Problem.
Conflict of interest
This Research Problem does not have any specified conflicts of interest.