What question did this study set out to answer?

To present an alternative proof demonstrating that the set of prime numbers includes arbitrarily long arithmetic progressions.

March 27, 2026Open Access

The Green-Tao Theorem

Key Points

To present an alternative proof demonstrating that the set of prime numbers includes arbitrarily long arithmetic progressions.
Provided a new mathematical proof approach for understanding prime sequences.
Analyzed the structure of primes in relation to integer sequences.
Confirms that primes can form arithmetic progressions of any length, enhancing previous findings.

Abstract

Preprint v1 — An alternative proof that the primes contain arbitrarily long arithmetic progressions. Abstract redacted pending IP review. Full abstract and unrestricted access will be available in v2 upon completion of intellectual property proceedings. Author: Joseph Keen Affiliation: Phoenix Quantum Labs LLC

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Cite This Study

Joseph R. Keen (Wed,) studied this question.

synapsesocial.com/papers/69c6209315a0a509bde191fe https://doi.org/https://doi.org/10.5281/zenodo.19216666