Hybrid Framework for Prime Number Prediction Using Fourier-Encoded Temporal Features and Self-Learning Models

Number theory is based on constructing new numbers out of fundamental building blocks, of which the first are prime numbers. Being deterministic, they do not constitute completely unexplored distributions of prime numbers. In this paper, we propose a new computational framework, Hybrid Prime Prediction Framework, which leverages advanced signal processing and adaptive machine learning techniques to predict prime numbers. The framework comprises two main modules, the Fourier Encoded Feature Extraction and the Self Learning Prime classifier. The Fourier Encoded Feature Extraction (FEFE) module uses Fast Fourier Transform (FFT) on sequences of prime gaps to convert these sequences into a frequency domain based on which it seeks latent periodicities and structural patterns that can usually be discerned only in the spatial domain. Then, the frequency domain features are taken as the inputs of the SLPC module—a lightweight online learning neural network that learns its parameters in a continuous online fashion based on the real time predictions outcomes. Furthermore, a Primality Score Function is defined to quantify how likely a given number is to be prime as the linear combination of its entropy, frequency strength, and local gap behavior. We demonstrate that experimental evaluation on the first hundred thousand prime numbers shows that HPPF provide higher accuracy, precision, recall, and F1 score than traditional static classifiers such as Decision Trees, SVM, and Feedforward Neural Networks. A novel data driven pathway to understanding prime distribution is provided in this work and a new modality for predicting number theory is opened.