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Prime numbers can be encoded using wave phenomena, similar to the Eratosthenes sieve. This research demonstrates how wave physics can generate the irregular prime number sequence from simple wave patterns.

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Area of Science:

  • Wave physics
  • Number theory
  • Quantum mechanics

Background:

  • The distribution of prime numbers is a fundamental problem in mathematics.
  • Prime number sieves, like Eratosthenes sieve, are classical methods for identifying primes.
  • Wave phenomena exhibit complex patterns that may relate to number sequences.

Purpose of the Study:

  • To encode the sequence of prime numbers using wave superpositions.
  • To explore the connection between diffraction physics and number theory.
  • To demonstrate a physical method for generating prime numbers.

Main Methods:

  • Encoding primes into superpositions of identical waves.
  • Identifying primes as zeros with phase singularities in wave fields.
  • Utilizing diffraction patterns from single apertures.
  • Analyzing harmonics of vibrating resonators.

Main Results:

  • Primes are encoded as zeros in wave fields with integer momenta.
  • Diffraction and resonator harmonics reveal prime number encoding.
  • Methods are shown for encoding Gaussian primes and twin primes.
  • Wave fields with amplitudes equal to the divisor function are constructed.

Conclusions:

  • Basic diffraction phenomena can generate the irregular sequence of prime numbers.
  • Simple, trivially ordered wave superpositions can produce prime number sequences.
  • Wave physics offers a novel perspective on the generation of prime numbers.