Representation of prime numbers on the complex plane

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Abstract

This study proposes a novel representation of prime numbers implying a quasiperiodic pattern within their distribution. Based on the result that any real number, and consequently, a prime number, can be represented in a complex plane using Euler’s notation; we investigated the quantities characterizing the sum of centres, which were observed as prime numbers. The numerical results indicate that prime numbers can be generated by rooting the real numbers, and their progression can be decomposed into periodic sequences. Within this framework, a harmonic prime function was identified, offering new insights into the structural intricacies of prime number sequences. The methodology employed advanced techniques to uncover the hidden periodicity underlying the quasiperiodic arithmetic progressions of primes, shedding light on the deeper patterns governing their distribution.

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