An Arithmetic Seismic Activity Model

There is a similarity between the distribution of prime numbers and the pattern of earthquake occurrence. Earthquakes occur in a discrete manner in time and space. When viewed as a whole, however, we find some laws, such as Gutenberg-Richter law, that govern the entire earthquakes that seem to be individually independent. A similar phenomenon can be observed also in the world of number. The most basic example is the distribution of the prime numbers in integers. We consider a correspondence between earthquakes and prime numbers. We parameterize occurrence time of earthquakes as the prime numbers and magnitude of earthquakes as the interval of prime numbers. Then we obtain a relationship similar to Gutenberg-Richter law. We call the model obtained by this correspondence as “arithmetic seismic activity model”. If we can parameterize earthquakes using prime numbers, knowledge that has been cultivated in the number theory can be used for understanding of earthquakes. The distribution of prime numbers is related to the distribution of zeros of Riemann zeta function. Researches are in progress to understand the zeros of the Riemann zeta function as an eigenvalue problem of quantum dynamical system. Earthquake may be modeled as a phenomenon corresponding to a change in the energy level of a quantum dynamical system associated with prime numbers.