Criticality in the counting function of prime numbers: Theory and application to nuclear magic numbers

In this paper, considering critical phenomena and their phase transitions within the frame of the set of prime numbers, is attempted. Thus, the novel, theoretical and purely mathematical Model of Criticality based on Prime Numbers is introduced. This approach allows for the emergence of a parallelism between the physical concept of criticality and the corresponding concept in prime number theory. Based on this parallelism an application of the proposed model in determining the known magic numbers of Nuclear Physics is presented. This application introduces a physical meaning to the exceptional in properties set of the prime numbers and the corresponding prime number theory. Finally, going beyond the proposed model and its application, we suggest investigating other prime numbers as doubly magic numbers or candidate magic numbers for further experimental research.

Automated summary

This paper attempts to consider critical phenomena and their phase transitions within the frame of the set of prime numbers. Thus, a novel, theoretical and purely mathematical Model of Criticality based on Prime Numbers is introduced. This model introduces a parallelism between the physical concept of criticality and the corresponding concept in prime number theory, and is applied in determining the known magic numbers of Nuclear Physics. The paper also suggests investigating other prime numbers as doubly magic numbers or candidate magic numbers for further experimental research.