ARIMA (p,d,q) and Non-Linear Approximation Models for the Fractal Dimension of the Density of Primes Less or Equal to a Positive Integer


  • Roberto N. Padua
  • Rodel B. Azura Mindanao University of Science and Technology
  • Mark S. Borres University of San Jose-Recoletos
  • Adriano V. Patac Jr. Surigao State College of Technology



time series model, fractal density of primes, autoregressive, moving average AMS Classification, Number theory, applied mathematics


The study compares the performance of the Azura et al. (2013) prediction model for the fractal dimension of the density of primes less or equal to a positive integer x with the performance of an autoregressive integrated moving average model (ARIMA(p,d,q). The actual density of primes used in this study were gathered from published table of primes . Results revealed that the time series model ARIMA(p,d,q) outperforms the Azura et al. (2013) prediction model particularly for larger values of X in the range of forecast values. The time series model is more convenient to use in practice since it only involves the previous calculated values of the fractal dimensions.

Author Biographies

Roberto N. Padua

Dr. Roberto Natividad Padua, scientist, received his PhD in Mathematical Statistics from Clemson University, South Carolina, USA under the Fullbright-Hays scholarship grant. He is an accomplished author, a multi-awarded researcher and an internationally acclaimed lecturer. Dr. Padua is a former Commissioner of CHED and currently a consultant to several state and private universities. He is also conducting lectures on research and Fractal Statistics. Dr. Padua is a Summa Cum Laude, BS in Mathematics Teaching graduate from the Philippine Normal College under the National Science Development Board (NSDB) program. He obtained his MS in Mathematics Education Degree from the Centro Escolar University as a Presidential Scholar.

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.


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How to Cite

Padua, R. N., Azura, R. B., Borres, M. S., & Patac Jr., A. V. (2013). ARIMA (p,d,q) and Non-Linear Approximation Models for the Fractal Dimension of the Density of Primes Less or Equal to a Positive Integer. Recoletos Multidisciplinary Research Journal, 1(2).




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