Title

Prime Gap Diagonals And Goldbach'S Conjecture

Keywords

Incompatible even; Missing evens; Prime doublets; Prime-gap diagonals; Translation group

Abstract

A display of the doubly infinite set of prime doublets (any two odd primes, equal or unequal) is illustrated. An argument for Goldbach's conjecture is introduced that implies that Goldbach's conjecture is valid, providing there are no missing evens in the display. Properties of prime gap diagonals and that of a fundamental symmetry of the display are argued that described that imply location of missing evens. The notion that an even is incompatible with its lead prime is introduced. Evens are partitioned according to the lead prime of their respective rows and a component of the hypothesis is established for the respective two sets. A translation group relevant to the prime-gap cts. A translation group is discussed relevant to the prime-gap diagonal. Numerical examples are included. As the prime number sequence has been shown to be quasi chaotic, a mathematical proof of Goldbach's conjecture does not exist. One may, however, construct a good argument for its validity. Namely, consistent within the limits set by this property. © 2011 Academic Publications, Ltd.

Publication Date

8-19-2011

Publication Title

International Journal of Pure and Applied Mathematics

Volume

70

Issue

7

Number of Pages

889-900

Document Type

Article

Personal Identifier

scopus

Socpus ID

80051691144 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/80051691144

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