Integers and Prime Numbers: Deriving Zipf's Law — mentioned by Xmd5a

Thu, 23 Jul 2026 14:51:18 GMT

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 Mandelbrot's rank-shifted model of Zipf's law and Riemann's Zeta function becomes Hurwitz Zeta function (ZetaHurwitz(s,a+1) with the ranks starting at 1). Zipf law != Zipf distribution, still this is intriguing. Integers and Prime Numbers: Deriving Zipf's Law (https://arxiv.org/abs/2403.12773) > In a prime number…

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Integers and Prime Numbers: Deriving Zipf's Law · HackerPapers discussions

Integers and Prime Numbers: Deriving Zipf's Law — mentioned by Xmd5a