Carregant...
Tipus de document
Treball de fi de màsterData de publicació
Llicència de publicació
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/99217
The complex architecture of primes and natural numbers
Títol de la revista
Autors
ISSN de la revista
Títol del volum
Resum
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
Descripció
Màster Oficial en Física Avançada, , Facultat de Física, Universitat de Barcelona, Curs: 2014, Tutors: M. Ángeles Serrano i Marián Boguñá
Matèries (anglès)
Citació
Col·leccions
Citació
GARCÍA PÉREZ, Guillermo. The complex architecture of primes and natural numbers. [consulta: 29 de novembre de 2025]. [Disponible a: https://hdl.handle.net/2445/99217]