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This research aims to provide a geometric framework for understanding primality and integer composition.

May 18, 2026Open Access

The First Geometric Definition of Primality: Cascade Floor-Touch and the Cascade Algorithm

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Randomized trial shows a new geometric definition of primality, highlighting the link between primes and their composition.

This research aims to provide a geometric framework for understanding primality and integer composition.
Establishes the Bounce Theorem for defining cascade residuals for integers.
Introduces Euler product ratio measures for prime cascade trajectories.
Defines a geometric structure linking primes and composites via the cascade mechanism.
Every prime has cascade residual cn(σ) = 0 at every depth σ > 0.
The geometric locus g∗ is the first shared address for all primes.
Integers are organized similarly to the chemical Periodic Table based on factor interactions.

Lucian Randolph (2026) studied this question.

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May 18, 2026Open Access

View Full Paper

Ask AI

Bookmark

Authors

Randomized trial shows a new geometric definition of primality, highlighting the link between primes and their composition.

This research aims to provide a geometric framework for understanding primality and integer composition.
Establishes the Bounce Theorem for defining cascade residuals for integers.
Introduces Euler product ratio measures for prime cascade trajectories.
Defines a geometric structure linking primes and composites via the cascade mechanism.
Every prime has cascade residual cn(σ) = 0 at every depth σ > 0.
The geometric locus g∗ is the first shared address for all primes.
Integers are organized similarly to the chemical Periodic Table based on factor interactions.

Lucian Randolph (2026) studied this question.

View Full Paper

Ask AI

Bookmark