On a Fractal Representation of the Density of Primes
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Center for Policy, Research and Development Studies
2014-12-01
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| Series: | Recoletos Multidisciplinary Research Journal |
| Subjects: | |
| Online Access: | https://rmrj.usjr.edu.ph/rmrj/index.php/RMRJ/article/view/96 |
| Summary: | 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. |
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| ISSN: | 2423-1398 2408-3755 |