The Exploring Primeness Project
Searching for degrees of primeness
This project is one of exploring primeness and developing the concept of primeness by looking at it from fresh perspectives.
If theoreticians of chaos have conceptualised dimensionality as a category that is continuous rather than discrete, and fuzzy logicians have developed similar concepts regarding truth and falsehood - not to mention Cantor's classes of infinity - we are investigating the differentiation of primeness.
Others, including the great Ramanujan, have studied the differentiation of compositeness. The term 'highly composite' is commonplace. Even thousands of years ago, it can only have been with the aid of such a concept that the number 60 was first chosen as an important base - one still used today in the measurement of time and geographical distance. Low or high compositeness may also be grasped by means of Euler's phi function.
Whilst we are sure that contributions will continue to be made in the theorisation of low compositeness as a form of high partial or relative primeness, we are not ourselves looking at the composite/prime duality. Rather, we are looking at primeness itself, specifically, and seeking to differentiate that concept within its very application to prime numbers. We are dispensing with the assumption that the study of primeness must always be dominated by the definition of primeness as the absence of compositeness. A comparison might well be drawn between primeness as it is normally understood, and the idea of 'absolute rest' with which some theologians have sought to grasp the concept of God. The view that it might be useful to develop concepts of 'high' or 'intense' primeness has not to our knowledge been given much consideration until now. By means of the Exploring Primeness Project we seek to help change this existing state of affairs.
We feel that the exploration has many potential implications in mathematics, metamathematics, aesthetics, and other fields. We wonder what Kurt Godel might have done with a concept of degrees of primeness had one been available at the time. Our findings and thoughts will be published here.
We welcome email (to primeness (at) borve (dot) org) from those who are interested in the project or who wish to contribute to it.
Texts at this site
Fernandez's Order of Primeness, F(p)
Some prime sequences related to F(p)
The prime-composite array, B(m,n), and the Borve conjectures
The Prime Pages
Copyright, Exploring Primeness Project, 1999, 2001, 2003, 2007
Last modified: 14 October 2007.