Patterns in Pythagorean Triples: A Computational Search for Rare Numerical Sequences

September 9, 2014Open Access

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This research aims to explore the distribution and patterns of Pythagorean triples, focusing on rare numerical sequences.
Implemented a computational search using C++ and GMP for large integers up to 10^12.
Analyzed gap sequences and density patterns in primitive hypotenuses through statistical and spectral analysis.
Utilized Bayesian normalization and a tree-based generation approach for efficient enumeration of triples.
Identified non-Poissonian gap distributions among hypotenuses, indicating rigid arithmetic structures.
Observed clustering phenomena in gap sequences, related to Gaussian prime properties.
Established that hypotenuse distribution displays a persistent local density rhythm dependent on prime factors.

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Explores Pythagorean triple distribution in integers, indicating structured numerical patterns.

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Ningappа К (2014) studied this question.

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