Notes on properties of binary strings which encode prime occurrences

2018/10/02 by Kajetan Młynarski, Młynarski, Kajetan
Computer Science · Mathematics · #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #math.NT #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1810.01445

arxiv created 2018/10/02 · openalex publication_date 2018/10/02 · arxiv updated 2018/10/04 · openalex created_date 2018/10/12 · openalex updated_date 2026/07/28

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.

Citations

• Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4⋅10¹⁸

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