%0 Journal Article
%T How Prime Numbers Are Interconnected and Built with Two Equations: Addition and Subtraction Rules the Function (6µ)
%A John Richard Wisdom
%J Advances in Pure Mathematics
%P 228-241
%@ 2160-0384
%D 2024
%I Scientific Research Publishing
%R 10.4236/apm.2024.144014
%X Are all prime numbers linked by four simple functions? Can we predict when a prime will appear in a sequence of primes? If we classify primes into two groups, Group 1 for all primes that appear before <i>ζ</i> (such that <img src=\"https://html.scirp.org//file/5302399-rId13.svg?20240416020453\" >, for instance 5, <img src=\"https://html.scirp.org//file/5302399-rId15.svg?20240416020453\" >), an even number divisible by 3 and 2, and Group 2 for all primes that are after <i>ζ</i> (such that <img src=\"https://html.scirp.org//file/5302399-rId17.svg?20240416020453\" >, for instance 7), then we find a simple function: for each prime in each group, <img src=\"https://html.scirp.org//file/5302399-rId19.svg?20240416020453\" >, where <i>n</i> is any natural number. If we start a sequence of primes with 5 for Group 1 and 7 for Group 2, we can attribute a <i>μ</i> value for each prime. The <i>μ</i> value can be attributed to every prime greater than 7. Thus <img src=\"https://html.scirp.org//file/5302399-rId21.svg?20240416020453\" > for Group 1, and <img src=\"https://html.scirp.org//file/5302399-rId23.svg?20240416020453\" >. Using this formula, all the primes appear for <img src=\"https://html.scirp.org//file/5302399-rId25.svg?20240416020453\" >, where <i>μ</i> is any natural number.
%K Number Theory
%K Prime Number Groups
%K Twin Primes
%K Prime Structure and Sequence
%K Prime Subtraction and Addition
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=132481