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Biot-Savart type magnetic field quantization via prime number theory, applications to symbolic dynamics

In the present work we propose an algorithm based on the theory of prime numbers for the estimation of the magnetic field in a device of current carrying circular rings. Using the proposed algorithm, the magnetic field can be determined in a very good agreement with that resulting from an algorithm based on the Biot-Savart law. In addition, the prime-numbers-based algorithm gives quantized values of the magnetic field and reveals previously unknown behaviors such as special properties of the distribution of the waiting times at the quantized magnetic field values. Applications of the proposed prime-numbers-based algorithm to systems exhibiting symbolic dynamics is presented, proving its ability to provide a measure of the existence or not of dynamics in the system.