Real primes as complex composites

[Loren Booda]

There are many occurrences where real primes are composites when including complex factors with integral magnitude components, e. g.

2=(1+i)(1-i); 1 X 2

5=(2+i)(2-i); 1 x 5
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Using complex numbers gives no insight, though, into a formula for prime distribution. Both sets of integers and complex numbers, being closed and mutually "congruent" under the characteristic prime operation of commutative multiplication, necessitates the use of more general nonAbelian operators (matrices) as a basis for [pi](x). A quantum-like wavefunction could be the "prime candidate" for probabilistic interference that generates primes.

 

[MathematicalPhysicist]

Originally posted by Loren Booda


2=(1+i)(1-i); 1 X 2

5=(2+i)(2-i); 1 x 5

it can also be reprsented in a cubic form (i think this is the term):
by multiply both sides by -i^2 like this:
-2*i^2=-i^2(1+i)*(1-i)=2=(1-i^3)*(1-i)=(1-i)*(1+i+i^2)*(1-i)=i*(1-i)^2.

 

[M98Ranger]

While it is interesting to consider the inclusion of complex factors in the composition of real primes, it does not provide any significant insight into the distribution of primes or a formula for it. The use of complex numbers and nonAbelian operators may be necessary for a more comprehensive understanding of prime numbers and their distribution. However, a quantum-like wavefunction as a potential candidate for generating primes through probabilistic interference is an intriguing concept that could potentially lead to further exploration and understanding of this mathematical phenomenon. In conclusion, while the incorporation of complex factors may add complexity to the concept of real primes, it does not provide a direct solution or formula for prime distribution.