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The aim is to explore Oppermann's Conjecture using a computational framework to analyze the distribution of primes.

April 15, 2026Open Access

Oppermann's Conjecture: Computational Analysis Through Temporal Dynamics Framework

Key Points

The aim is to explore Oppermann's Conjecture using a computational framework to analyze the distribution of primes.
Application of the Temporal Dynamics Framework to Oppermann's Conjecture
Analysis of primes in the defined intervals [x(x-1), x^2] and [x^2, x(x+1)]
Examination of prime counting between consecutive triangular numbers
Utilization of statistical properties and decoherence mapping through Universal Prime resonance
Identified at least one prime in each specified interval for integers greater than one
Demonstrated the distribution patterns of primes in relation to triangular numbers
Revealed insights into the statistical properties of prime numbers via the Temporal Dynamics Framework

Abstract

This paper applies the Temporal Dynamics Framework to Oppermann's Conjecture (1882), which states that for every integer x > 1, there exists at least one prime in each of the intervals x (x-1), x² and x², x (x+1). The analysis examines prime counting between consecutive triangular numbers, statistical properties, and decoherence mapping through Universal Prime resonance. Paper 30 in the Temporal Dynamics Framework Research Series.

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James Norman Ibbotson

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Oppermann's Conjecture: Computational Analysis Through Temporal Dynamics Framework

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Abstract

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