The system of prime coordinates assigned to the positive integers

Silviu Guiasu
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 24, 2018, Number 2, Pages 1–5
DOI: 10.7546/nntdm.2018.24.2.1-5
Full paper (PDF, 136 Kb)

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Authors and affiliations

Silviu Guiasu
Department of Mathematics and Statistics, York University
4700 Keele Street, Toronto, Ontario M3J 1P3, Canada

Abstract

Due to the fundamental theorem of number theory, the positive integers may be represented by vectors whose components are the unique corresponding powers of the prime numbers. Taking the prime numbers as coordinates, to each positive integer we assign a prime vector, whose components are the powers of the prime factors of this integer. The geometry of this system of prime coordinates of the positive integers is discussed. It is shown that the prime components assigned to the sequence of positive integers change in a strictly deterministic way and the parallel generating system is presented. Gödel’s prime vectors assigned to formal logical formulas are analyzed.

Keywords

• Prime coordinates
• Prime vectors
• Regular structure of the prime coordinates
• Parallel generating system
• Gödel’s prime vectors

2010 Mathematics Subject Classification

• 11A41

References

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4. Guiasu, S. (2009) Probabilistic Models in Operations Research, Nova Science Publishers, New York.
5. Nagel, E., & Newman, J. R. (1958) Gödel’s Proof. The New York University Press, New York.