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Title: The complex architecture of primes and natural numbers
Author: García Pérez, Guillermo
Director: Serrano Moral, Ma. Ángeles (María Ángeles)
Boguñá, Marián
Keywords: Nombres naturals
Xarxes complexes (Matemàtica)
Tesis de màster
Processos estocàstics
Natural numbers
Complex networks (Physics)
Masters theses
Stochastic processes
Issue Date: Dec-2014
Abstract: Natural numbers can be divided in two non-overlapping infinite sets, primes and composites, with composites factorizing into primes. Despite their apparent simplicity, the elucidation of the architecture of natural numbers with primes as building blocks remains elusive. Here, we propose a new approach to decoding the architecture of natural numbers based on complex networks and stochastic processes theory. We introduce a parameter-free non-Markovian dynamical model that naturally generates random primes and their relation with composite numbers with remarkable accuracy. Our model satisfies the prime number theorem as an emerging property and a refined version of Cramér's conjecture about the statistics of gaps between consecutive primes that seems closer to reality than the original Cramér's version. Regarding composites, the model helps us to derive the prime factors counting function, giving the probability of distinct prime factors for any integer. Probabilistic models like ours can help to get deeper insights about primes and the complex architecture of natural numbers
Note: Màster Oficial en Física Avançada, , Facultat de Física, Universitat de Barcelona, Curs: 2014, Tutors: M. Ángeles Serrano i Marián Boguñá
Appears in Collections:Màster Oficial - Física Avançada

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