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.