The Relativity of Prime Numbers: Grid-Dependent Distributions and Cryptographic Applications

This paper challenges the foundational status of prime numbers in number theory, presenting them as coordinate-dependent artifacts of an arbitrary discrete measurement system rather than universal constants. Consistent with the continuous "Field Medium" paradigm, we demonstrate through non-unitary Hilbert monoids (such as the Even-Stepper grid) that both absolute physical values and relative sequence indices of primes shift completely based on the observer's step size. Finally, the paper introduces Dynamic Grid Cryptography (DGC) as a novel cryptographic framework that avoids standard integer-based quantum decryption algorithms (Shor's Algorithm) by shifting the baseline mathematical dimensions of encryption keys.

Keywords: Number Theory, Prime Numbers, Cryptography, Shor's Algorithm, Quantum Decryption, Epistemic Pluralism, Hilbert Monoids, Non-Unitary Grids