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March 27, 20260 citationsOpen Access

Legendre's Conjecture

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JKJoseph R. Keen

Key Points

  • The aim is to prove that there is always at least one prime number between n² and (n+1)² for every positive integer n.
  • Mathematical proof techniques
  • Analytical reasoning
  • Exploration of prime distributions
  • Proves the existence of a prime number between the specified intervals for all n
  • Validates Legendre's Conjecture

Abstract

Preprint v1 — A proof that there is always a prime between n² and (n+1)² for every positive integer n. 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/69c6206115a0a509bde18e2ehttps://doi.org/10.5281/zenodo.19216453
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