Mathematica Eterna
Open Access

Department of Mathematics and Statistics, McGill University, Quebec, Canada

Publications

• Review Article   
  Stochastic Characterization and Numerical Analysis of Prime Gaps for Stationary Distribution Approximation
  Author(s): George Gabriel*
  
  This paper presents a comprehensive stochastic framework for modeling the Probability Mass Function (PMF) of prime gaps, focusing on the existence and characterization of a stationary distribution. Through theoretical analysis, we establish that prime gap sequences can be effectively modelled as stochastic processes and provide a formal proof of the existence of a stationary distribution that governs their long-term behavior. To support our theoretical findings, we conducted an extensive numerical analysis using the Canadian supercomputer "Béluga", computing prime gaps up to 1012 using the Sieve of Eratosthenes. The empirical results validate our models, particularly those incorporating arithmetic properties such as prime factorization and modulo 6 congruence, demonstrating that they capture the periodic and combinatorial nature of .. View More»
  DOI: 10.35248/1314-3344.24.14.236

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