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The research aims to establish a geometric and spectral approach to the Twin Prime Conjecture, exploring prime number distribution.

March 28, 2026Open Access

A Geometric-Spectral Framework for the Twin Prime Conjecture: Symmetry Invariance and Prime Reflection Waves

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This theoretical framework demonstrates spectral stability in primorial rings, suggesting implications for twin prime distribution.

The research aims to establish a geometric and spectral approach to the Twin Prime Conjecture, exploring prime number distribution.
Introduced the Speckmann Framework focusing on spectral stability and geometric invariants.
Analyzed prime numbers as harmonic oscillations within Hilbert space.
Utilized an Exclusion Formula to filter potential twin prime positions.
Conducted numerical stress tests on NVIDIA T4 GPUs for verification.
Demonstrated a positive spectral lower bound related to twin prime distribution.
Achieved nearly perfect uniform distribution of residues with only a 0.10% deviation from statistical ideal.
Indicated that the infinitude of twin primes is necessary for the spectral continuity of integers.

Daniel Speckmann (2026) studied this question.

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