The Density of Primes Less or Equal to a Positive Integer up to 20,000: Fractal Approximation

Authors

  • Rodel B. Azura Mindanao University of Science and Technology
  • Dennis A. Tarepe Mindanao University of Science and Technology
  • Mark S. Borres University of San Jose-Recoletos
  • Jocelyn T. Panduyos Surigao del Sur State University

DOI:

https://doi.org/10.32871/rmrj1301.02.21

Keywords:

density of primes, prime number theorem, multifractal distribution AMS classification, number theory, applied mathematics

Abstract

The highly irregular and rough fluctuations of the number of primes less or equal to a positive integer x for smaller values of x ( x≤20,000) renders the approximations through the Prime Number Theorem quite unreliable. A fractal probability distribution more specifically, a multifractal fit to the density of primes less or equal to x for small values of x, is tried in this study. Results reveal that the multifractal fit to the density of primes in this situation outperforms the Prime Number Theorem approximation by almost 200% viz. the
prediction error incurred by using the PNT approximation is double that of the multifractal fit to the density of primes. The study strongly suggests that a better multifractal distribution exists, even for large x, than the Prime Number approximation to the density of primes.

Author Biography

Mark S. Borres, University of San Jose-Recoletos

graduated Bachelor of Science in Mathematics–major in Pure Mathematics at the University of the Philippines, Cebu College. Since 2009, he worked for the University of San Jose- Recoletos as a faculty member of the College of Arts and Sciences and handled Mathematics subjects such as College Algebra, Advanced Algebra, Abstract Algebra, Analytical Geometry, Euclidean geometry, Trigonometry, Business Mathematics, Linear Programming, Mathematics of Investment, Discrete Structure, and Statistics across colleges.

References

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Published

2013-12-31

How to Cite

Azura, R. B., Tarepe, D. A., Borres, M. S., & Panduyos, J. T. (2013). The Density of Primes Less or Equal to a Positive Integer up to 20,000: Fractal Approximation. Recoletos Multidisciplinary Research Journal, 1(2). https://doi.org/10.32871/rmrj1301.02.21

Issue

Vol. 1 No. 2 (2013)

Section

Articles

License

Copyright of the Journal belongs to the University of San Jose-Recoletos