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arXiv:2403.12773physics.soc-ph

Integers and Prime Numbers: Deriving Zipf's Law

Helmut Satz

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Abstract

In a prime number decomposition of integers in a given set, the occurrence frequencies of prime numbers are shown to satisfy a general forms of Zipf's law.

arXiv comments
Journal reference
DOI
Subjects
physics.soc-phPhysics and Society math.NTNumber Theory

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  1. What does the Riemann zeta function have to do with the distribution of primes? 1 comment

    • The link is between numbers and words. Both can be decomposed into primitive components: primes and lyndon words (combinatorics). The Zipf distribution takes this shape when the vocabulary is infinite: P(r)=r^-s / Zeta(s) with s > 1 Replace r^-s with (r + a)^-s, i.e. move onto…

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