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The Prime Isolation Engine (PIE): A Deterministic Approach to Prime Prediction

24 March 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This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.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

This document presents the formal structure of the Prime Isolation Engine (PIE), a deterministic framework for prime prediction that integrates modular composite exclusion (PRT) with prime gap classification (PGT). By rigorously excluding composite structures and validating structural gap types, PIE defines a repeatable mechanism for isolating primes across 𝑁.

Keywords

Prime Isolation Engine (PIE)
Deterministic Prime Prediction
Prime Remainder Theorem (PRT)
Prime Gap Type (PGT)
Composite Neighborhood (CN)
Prime Gaps
Structural Number Theory
Modular Exclusion

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Version History

Mar 24, 2025 Version 1

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License

All Rights Reserved

DOI

10.33774/coe-2025-pz7zx
D O I: 10.33774/coe-2025-pz7zx [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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