### 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 compared 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

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