The Prime Resolution Function

We propose a finite, compressibility-based function for detecting prime numbers, grounded in the principle that primes are structurally irreducible entities, the least amenable to resolution by divisibility. This function, the Prime Resolution Function Ψ(n), measures the entropy of a natural number by summing weighted divisors up to √n, and inverting that score to reflect structural resistance. Unlike traditional approaches relying on infinite series or analytic continuation, our model is constructivist and entropy-aware. We further argue that the Riemann Hypothesis, while analytically elegant, is structurally overparameterized; its non- trivial zeros do not directly represent primes but describe them asymptotically. Our framework offers an information-theoretic alternative in which primality is not inferred, but measured through finite resolution logic.