Luque, B. and Lacasa, L. (2009) The First-Digit Frequencies of Prime Numbers and Riemann Zeta Zeros. Proceedings of the Royal Society A, 564, 2197-2216.
https://doi.org/10.1098/rspa.2009.0126

has been cited by the following article:

• TITLE: Regular Decimations Result in Irregular Distribution of Primes

  AUTHORS: Xin Wang

  KEYWORDS: Primes, Composites, Complementary, Periodicity, Super Product, Fourier Transform

  JOURNAL NAME: Advances in Pure Mathematics, Vol.12 No.6, June 28, 2022

  ABSTRACT: Purpose: Primes are notorious for their irregular distribution in natural numbers. Such a lack of regularity makes primes elusive. Many NP-hard problems are related to the irregular occurrence of primes in natural numbers. Methods: To extract the underlying regularity of prime distribution, author started from the complementary relationship between composites and primes, through the regular occurrence of composites to infer the regularity underlying primes. Results: Previously random-appearing occurrence of primes resulted from the regular periodic decimations of various frequencies and cycles set by primes. Conclusions: Primes are the survivors of natural numbers after periodic decimations caused by primes. This leads to a novel concise representation of the set of all primes using sine function, suggestive of periodicity for both primes and composites.