On a Fractal Representation of the Density of Primes

Authors

  • Joy Mirasol Bukidnon State University
  • Efren O. Barabat University of San Jose-Recoletos

DOI:

https://doi.org/10.32871/rmrj1402.02.13

Keywords:

fractal density, prime number theorem, Riemann hypothesis

Abstract

The number of primes less or equal to a real number x, π(x), has been approximated in the past by the reciprocal of the logarithm of the number x. Such an approximation works well when x is large but it can be poor when x is small. This paper introduces a fractal formalism to provide more fl exible approximation to the density of primes less or equal to a number x using the λ(s)-fractal spectrum. Results revealed that the density of primes less than or equal to x can be modeled as a monofractal probability mass function with high
fractal dimension for large x. High fractal dimensions can often be decomposed to form a multifractal representation. The fractal density representation of the density of primes is closely linked to the Riemann zeta function and, thus, to the famous unsolved Riemann hypothesis.

Author Biography

Efren O. Barabat, University of San Jose-Recoletos

is an Electronics Engineer, graduated from the University of San Jose-Recoletos in 2010, Cum Laude honors. He ranked as top 9 examinee in the April 2011 ECE Licensure Examination. He worked as Field Engineer in SMART Communications, Inc. from 2011 to 2012. Currently, a full-time faculty member of the Electronics Engineering Department of USJ-R College of Engineering, handling Mathematics and Major Subjects of ECE.

References

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Published

2014-12-28

How to Cite

Mirasol, J., & Barabat, E. O. (2014). On a Fractal Representation of the Density of Primes. Recoletos Multidisciplinary Research Journal, 2(2). https://doi.org/10.32871/rmrj1402.02.13

Issue

Vol. 2 No. 2 (2014)

Section

Articles

License

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

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