Formula for Odd Prime Numbers

This paper presents a structural variant of explicit Willans-type formulasfor generating the n-th prime number pn. Through the integration of an arithmetic filtering kernel based on floor function differences, an indexed accumulation operator, and an outer linear transformation, a deterministic analyticalexpression is established that accurately maps the sequence of prime numbersin the domain pn ≥ 5. The three fundamental expressions composing thecomputational system are detailed.