# name
The complex architecture of primes and natural numbers

# metadata.dc.contributor.advisor[].value
Serrano Moral, Ma. Ángeles (María Ángeles)

# metadata.dc.description[].value
Màster Oficial en Física Avançada, , Facultat de Física, Universitat de Barcelona, Curs: 2014, Tutors:  M. Ángeles Serrano i Marián Boguñá

# metadata.dc.description.abstract[].value
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

# metadata.dc.title[].value
The complex architecture of primes and natural numbers