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

Abstract

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.

Keywords

• time series model
• fractal density of primes
• autoregressive
• moving average ams classification
• number theory
• applied mathematics