We believe that it is quite possible to realize this using a dimensionless constant LAMBDA that would depend on prime numbers. Under these conditions, a new reduced h/h ratio would be a function of LAMBDA; under these conditions, the constants of the quantum world and the cosmological parameters, notably LAMBDA and OMEGA, would be a function of prime numbers. The speed of light in a vacuum would also be a function of prime numbers. EVEN THE BOLTZMANN CONSTANT WOULD BE SOMEHOW A FUNCTION OF PRIME NUMBERS, ETC.
From a number theory viewpoint, it is known that any number can approximated arbitrarily closely by the ratio of two primes, so what you suggest would be true to any level of experimental error, but you can say the same about any number.
No. Models of natural phenomena express symmetries, the transformations that leave the equations of motion invariant. The description of these transformations is, of course, an expression of mathematics, so prime numbers do play a role, that is much more indirect, however.
The preprints* show that it is absolutely possible to obtain absolute physical constants using prime nupmbesr notable the prime number 19.
*Preprint: Absolute Frequencies of Strontium Atomic Clocks from Theoretical Dimensionless Ratios of Strontium frequencies to Quartz Frequency.
*Preprint: An Absolutely Exact Duration in seconds of the Sidereal day, or Stellar day, emerging from an Irreducible Numerical Ratio from Ultimate Cosmology, Astronomy, and Astrophysics.
*Preprint: An Irreducible Numerical Ratio for the Duration in Days of the Mean Sidereal Year via Ultimate Cosmology, Astronomy, and Astrophysics
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