Goldbach Circles and Balloons and Their Cross Correlation

TL;DR

This paper explores properties of Goldbach-based geometric sequences, revealing their strong randomness and minimal correlation, making them suitable for cryptographic and spread spectrum applications.

Contribution

It extends Goldbach partition analysis to concentric circles, analyzing their properties and correlation characteristics for cryptographic use.

Findings

Sequences exhibit excellent randomness properties.

Cross correlation indicates minimal dependencies.

Suitable for cryptographic applications.

Abstract

Goldbach partitions can be used in creation of ellipses and circles on the number line. We extend this work and determine the count and other properties of concentric Goldbach circles for different values of n. The autocorrelation function of this sequence with respect to even and odd values suggests that it has excellent randomness properties. Cross correlation properties of ellipse and circle sequences are provided that indicate that these sequences have minimal dependencies and, therefore, they can be used in spread spectrum and other cryptographic applications.