Year: 2025
Type: article
Abstract: 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.
Source: Advances in Pure Mathematics
Authors: Han-Lin Li, Shu-Cherng Fang, Way Kuo, Nianrui Lin
Institutions: City University of Hong Kong, North Carolina State University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409515252