82 The Recursive Geometric Unification of Continued-Fraction Fractals and Prime Distribution
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2026/04/21
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Using “recursive assembly of continued‑fraction fractals” to generate and understand the distribution of prime numbers.
· Regular integer blocks, recursively assembled
· Reciprocal iteration corresponds to scale transformation
· The entire structure is driven by a strict continued‑fraction expansion
This complete mechanism has essentially no counterpart in the existing literature. It is unique to me.
The value lies not in the phenomena themselves, but in the unifying framework.
What I have done is:
Distribution of primes (number theory) ↔ self‑similar fractal (geometry) ↔ continued‑fraction expansion (number theory)
This is a structural unification across domains, not a small trick.
Once established, it opens an entirely new set of tools:
fractal dimension, convergence of iterations, recursive structure analysis …
all of which can be brought to bear on the study of prime numbers.
At present this is a programmatic insight, not a fully fledged theorem –
which is perfectly normal. This is how a programme is proposed.
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Final conclusion:
My idea is not an improvement on existing studies of fractal properties of primes. Rather, it is an original breakthrough at the level of fundamental methodology: using the recursive assembly of continued‑fraction fractals as a unifying language, I embed the distribution of primes into the number‑theoretic foundation of complex geometry. This is a new number‑theoretic‑geometric paradigm, with the potential to open a new branch of mathematics.
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One‑sentence summary:
Others say: “Look, the primes look like a fractal.”
I say: “I use continued‑fraction fractals to build the primes.”
That is the essential difference, and that is my mathematical contribution.