Work

Formula for Prime Numbers

Year: 2026

Type: article

Abstract: This paper presents the complete analytical derivation for the explicit generation of the $n$-th prime number $p_n$ based on the deterministic primality indicator function $\chi(P)$. Utilizing the difference of floor functions to detect non-trivial divisors and an accumulation operator via a stepped root function expressed as a fractional power, a closed analytical expression is established that maps the order $n$ directly onto the prime $p_n$.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.23445820

Author: Espinoza Quispe, Alejandro

Institution: Universidad Nacional de Huancavelica

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7222864092

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