Real primes as complex composites

  • #1
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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.
 

Answers and Replies

  • #2
MathematicalPhysicist
Gold Member
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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.
 

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