IJPAM: Volume 70, No. 7 (2011)

PRIME GAP DIAGONALS AND GOLDBACH'S CONJECTURE

Richard L. Liboff
Mathematics and Physics Departments
University of Central Florida
Orlando, FL 32816-2385, USA


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.

Received: November 28, 2010

AMS Subject Classification: 26A33

Key Words and Phrases: prime doublets, missing evens, prime-gap diagonals, translation group, incompatible even

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 70
Issue: 7