A New Prime Number Theory

Not a real one, obviously (I'm neither a genius mathematician nor a crazy person, after all); but a fictional one, for a story I'm, distantly, planning. In my fictional future world, numbers are written not as binomial fractions, but as delta, hyperdelta and inverted hyperdelta forms. Instead of a line separated numerator and denominator as in a regular fraction, a triangular fraction constellates three numbers around a Δ. Hyperdelta fractions add two extra numbers in particular relation to the three, which can be thought of as in the third dimension. For an inverted hyperdelta fraction you must imagine a fourth dimension, in which imaginary numbers exist in superposition with the five numbers of a hyperdelta fraction. When construed as, alternativelt, hyperdelta and inverted hyperdelta fractions, all prime numbers show complex but regular patterning.