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March 27, 20260 citationsOpen Access

Wilson's Theorem

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JKJoseph R. KeenUniversity of California, Riverside

Key Points

  • The aim is to establish a proof that (p-1)! ≡ -1 (mod p) uniquely characterizes prime numbers.
  • Theoretical proof of Wilson's Theorem using definitions from modular arithmetic and number theory.
  • Demonstrated that the factorial of (p-1) modulo prime p equals -1 only for prime values of p.

Abstract

Preprint v1 — A proof that (p-1)! ≡ -1 (mod p) if and only if p is prime. 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 (2026) studied this question.

synapsesocial.com/papers/69c6207d15a0a509bde18eaehttps://doi.org/10.5281/zenodo.19216815
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