What question did this study set out to answer?

The research aims to explore additive prime comb potentials for encoding prime number distribution.

March 27, 2026Open Access

Additive Prime Comb Potentials Universal Tool for Additive Structure Encoding

Key Points

The research aims to explore additive prime comb potentials for encoding prime number distribution.
Developed additive combs to represent prime spacing and gaps using phase-aligned cosine series.
Applied the Prime Number Theorem to support non-circular construction of additive encoding.
Verified the model through numerical analysis on 100,000 twin prime pairs and 1,000,000 integers.
Demonstrated accurate representation of prime gaps in line with the Cramér conjecture and Goldbach's decompositions.
Showed less than 2% deviation from Benford's law in numerical tests, confirming model validity.

Abstract

Theory of additive prime comb potentials encoding prime number distribution in spectral operators through fractal logarithmic-scale oscillations. Unlike multiplicative combs (encoding factorization), additive combs capture spacing and gap distribution of primes through phase-aligned cosine series. Non-circular construction relying only on the Prime Number Theorem. Applications to prime gaps (Cramér conjecture), twin primes, and Goldbach decompositions. Numerical verification on 10⁵ twin prime pairs and 10⁶ integers (Benford's law, <2% deviation).

Connected Papers

Building similarity graph...

Analyzing shared references across papers

Discussion

Authors

Thierry Marechal

Actions

Institutions

F5 Networks (United States)

References and Citations

Connected Papers

Building similarity graph...

Analyzing shared references across papers

Additive Prime Comb Potentials Universal Tool for Additive Structure Encoding

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Authors

Actions

Institutions

References and Citations

Citation Network

Connected Papers

Discussion

Cite this study