Year: 2018
Type: preprint
Abstract: A binary string representation of prime occurrences is a sequence of bits, where $1$ entries encode positions of prime numbers. This is a convenient representation for analysis of prime distribution, since it allows for application of a broad range of existing string-analysis algorithms to problems in number theory. Binary strings of prime occurrences can be also generated with simple algorithms. Here we discuss three such algorithms and we demonstrate their applicability using the example of proving Goldbach's hypothesis for some limited sets of even numbers. This work formulates three open questions (conjectures) regarding the distribution of primes.
Source: arXiv (Cornell University)
Author: Młynarski, Kajetan
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2894927576