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February 5, 20260 citationsOpen Access

Himangshu-Aditya Conjecture

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ADAditya das Aditya dasHHHimangshu Himangshu

Key Points

  • The conjecture aims to explore the relationship between perfect squares and the distribution of prime numbers.
  • Defines the relationship between perfect squares and prime number pairs.
  • Proposes a symmetry where each perfect square is central to two surrounding primes.
  • Suggests that primes may not be randomly distributed but exhibit a structured pattern.
  • Presents a theoretical framework suggesting perfect squares are natural centers for prime pairs.
  • Indicates a potential geometric and arithmetic harmony in number distribution.
  • If proven, reveals a deep underlying order in prime number distribution.

Abstract

The Himangshu Aditya Conjecture, also known as the Square Prime Symmetry Conjecture, describes a proposed symmetry between perfect squares and prime numbers. It states that every perfect square is positioned at the exact midpoint between two prime numbers located at equal distances on either side. This conjecture suggests that perfect squares act as natural centers around which prime pairs are symmetrically arranged. Rather than appearing randomly, prime numbers may exhibit a structured balance when viewed relative to square numbers. If true, the conjecture would indicate a deep underlying order in the distribution of primes, revealing a consistent geometric and arithmetic harmony within the number system.

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Cite This Study

das et al. (2026) studied this question.

synapsesocial.com/papers/698434ebf1d9ada3c1fb3af5https://doi.org/10.5281/zenodo.18453889
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Kusniec's Theorem: Demonstrating Prime Numbers Between Squares and the Two Adjacent Oblong Numbers2024
  2. 2A Square Root Parity Classification of Primes2025
  3. 3A Square Root Parity Classification of Primes2025
  4. 4A Square Root Parity Classification of Primes2025
  5. 5MacMahon Convolutions and a Divisor-Gap Reformulation of the Twin Prime Conjecture2026