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TWINION: Symbolic Recurrence of Irreducible Prime Pairs

25 May 2025, Version 1
Working Paper
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

We prove the infinitude of twin primes using a symbolic framework known as the Abdeslam Irreducible Order of Naturals (AION). In this system, numbers are generated via prioritized multiplication, and symbolic irreducibility coincides with classical primality. We show that symbolic failures occur in pairs separated by two, leading to a deterministic structural proof of the Twin Prime Conjecture.

Keywords

Twin primes
Symbolic irreducibility
Prime gaps
AION
Number theory
Deterministic primality
Classical prime equivalence

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Version History

May 25, 2025 Version 1

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License

All Rights Reserved

DOI

10.33774/coe-2025-s7kn4
D O I: 10.33774/coe-2025-s7kn4 [opens in a new tab]

Author’s competing interest statement

The author(s) have declared they have no conflict of interest with regard to this content

Ethics

The author(s) have declared ethics committee/IRB approval is not relevant to this content

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