A speculative study of anomalous relaxation modeling for the distribution of prime numbers

Abstract

Nowadays, many researchers are puzzled by the problems about prime numbers, not only due to its complex and unknown characteristics, but also because it is difficult to construct a model to describe the relaxation distribution of prime numbers in the set of all natural numbers. To the best knowledge of authors, although some phenomenological methods, such as the Riemann's Theory, can describe the distribution of the prime numbers accurately, the law for the distribution of the prime numbers is not clear and the governing model has not founded until now. In the present study, for the first time, we employ anomalous relaxation model with the fractional derivative to obtain the distribution of prime numbers. The comparison with Prime Number Theory and Riemann's Theory show that the new model agrees well with the data of prime numbers.