Number Theory

    

Quadratic Inequality for Solving the Prime Gap Problem and Proving the Binary Goldbach Conjecture

Authors: Samuel Bonaya Buya

In this paper an identity is established connecting to consecutive primes. Bertrand’s postulate is used together with the identity to establish a quadratic inequality that can be used to establish minimum intervals containing at least three primes in between its limits. A generalization of the quadratic inequalityis introduced to establish the minimum interval containining at least one pair of primes for Goldbach partitition. The concepts of Goldbach partition deviation and Goldbach partition interval are introduced by which it is shown that the minimum number of Goldbach partitions of a composite even number is 1.

Comments: 23 Pages.

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[v1] 2025-01-29 03:17:34

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