Computing $\pi(x)$ Analytically

TL;DR

This paper presents a rigorous implementation of an analytic method to compute the prime counting function, successfully calculating the number of primes less than 10^24 using a proven mathematical approach.

Contribution

It introduces a precise implementation of the Lagarias and Odlyzko method for evaluating π(x), enabling large-scale prime counting without assumptions.

Findings

Successfully computed primes less than 10^24

Validated the analytic method's accuracy

Provided a framework for future large-scale prime computations

Abstract

We describe a rigorous implementation of the Lagarias and Odlyzko Analytic Method to evaluate the prime counting function and its use to compute unconditionally the number of primes less than $10^{24}$.