Real primes as complex composites

1. Nov 26, 2003

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.

2. Nov 27, 2003

MathematicalPhysicist

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.