Computing π(x) Analytically

2012/03/26 by David J. Platt, Platt, David J.
Computer Science · Engineering · Mathematics · #11N56 (Secondary) #11Y35 (Primary) 11N37 #Analytic Number Theory Research #Coding theory and cryptography #Computability, Logic, AI Algorithms #FOS: Mathematics #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1203.5712

openalex publication_date 2012/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 10²⁴.

Citations

• Explicit Bounds for Some Functions of Prime Numbers

Related

• An improved analytic Method for calculating π(x)
• An algorithm for the prime-counting function of primes larger than three
• The combinatorial algorithm for computing pi(x)
• A Simple Closed-Form Approximation to the Prime-Counting Function
• New bounds for the prime counting function π(x)