%0 Journal Article
%T Listing Prime Numbers Periodically
%A Han-Lin Li
%A Shu-Cherng Fang
%A Way Kuo
%A Nianrui Lin
%J Advances in Pure Mathematics
%P 247-268
%@ 2160-0384
%D 2025
%I Scientific Research Publishing
%R 10.4236/apm.2025.154012
%X Over millennia, people have considered prime numbers as unpredictable and hard to list. This study confirms that all positive integers without factors of 2, 3, 5 and 7 can be regarded as the offspring of 48 roots in the interval [11, 220]. These roots are to generate a Factor-Pair Table composed of 48 columns, each of which forms a basic binary matrix to indicate the locations of composite numbers. For a given interval, these composites are removed via mapping effect. After primality checking of the rest of the numbers, we identify all primes within the interval. We then form a Formula of Primes for prime prediction. Moreover, the Periodic Table of Primes (PTP) [1] is reconstructed based on the proposed algorithm to illustrate the distribution of primes and composites.
%K Prime Listing
%K Factor-Pair Table
%K Mapping Effect
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=141958