Dr
Fraile Alberto
(Department of Control Engineering. Faculty of Electrical Engineering, Czech Technical University in Prague)
The distribution of prime numbers is clearly very complex, and it research history has shown that solid proven conclusions about its structure will probably take a long time to come by. Before that happens, the field is in need of ideas able to provide an intuitive and qualitative understanding.
It is beyond the scope of this talk to provide quantitative results. Its main purpose is to offer the Mathematics community a simple model that can be used to explore the ideas we point out, which are interconnected with the most important unsolved problems related to the distribution of prime numbers.
In addition, technological implications of this study could be derived, since the Ladder scheme presents an excellent framework for developing pseudo-random number routines and randomness tests and algorithms.
Summary
Prime numbers are one of the most intriguing figures in mathematics. Despite centuries of
research, many questions remain still unsolved. In recent years, computer simulations are playing a
fundamental role in the study of an immense variety of problems. In this work, we employ that to present
a simple representation of prime numbers in two dimensions that allows us to formulate a number of
conjectures that may lead to important avenues in the field of research on prime numbers. In particular,
although the zeroes in our representation grow in a somewhat erratic, hardly predictable way, the gaps
between them present a remarkable property: there is a clear exponential decay in the frequency of the
gaps vs gap size. The smaller the gaps, the more frequently they appear.
References
https://arxiv.org/pdf/1801.01540.pdf
Dr
Fraile Alberto
(Department of Control Engineering. Faculty of Electrical Engineering, Czech Technical University in Prague)
Dr
Martinez Daniel
(University of Iceland)
Dr
Martinez Roberto
(Universidad del País Vasco)
