What question did this study set out to answer?

The aim is to investigate Sierpinski numbers using the Temporal Dynamics Framework and uncover their properties.

April 15, 2026Open Access

Sierpinski Numbers: Computational Analysis Through Temporal Dynamics Framework

Key Points

The aim is to investigate Sierpinski numbers using the Temporal Dynamics Framework and uncover their properties.
Applied the Temporal Dynamics Framework to analyze Sierpinski numbers
Executed resonance comparison and decoherence mapping
Conducted tier analysis and density scaling
Performed gap analysis and Universal Prime layer analysis
Completed 123 verification tests with all passing
Identified the smallest known Sierpinski number as k = 78557
Outlined properties of covering sets and their structures
Presented eight diagnostic figures illustrating key findings

Abstract

This paper applies the Temporal Dynamics Framework to Sierpinski numbers and covering sets. A Sierpinski number is an odd positive integer k such that k times 2ⁿ + 1 is composite for all positive integers n. The smallest known Sierpinski number is k = 78557. The analysis includes resonance comparison, decoherence mapping, tier analysis, covering set structure, density scaling, gap analysis, and Universal Prime layer analysis. All 123 verification tests pass. Eight diagnostic figures are included. Paper 36 in the Temporal Dynamics Framework Research Series.

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James Norman Ibbotson

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Sierpinski Numbers: Computational Analysis Through Temporal Dynamics Framework

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