What question did this study set out to answer?

The aim is to develop efficient algorithms for counting prime numbers up to a specified integer using Python.

March 14, 2026Open Access

A High-Performance Prime Counting Algorithm Implemented in Python

Key Points

The aim is to develop efficient algorithms for counting prime numbers up to a specified integer using Python.
Documented four algorithmic generations of the Ashik-Wheel Segmented Sieve (AWSS).
Analyzed performance improvements with each subsequent version.
Implemented algorithms in Python for accessibility and practicality.
Demonstrated significant performance enhancements in prime counting efficiency.
Identified weaknesses in predecessor algorithms and addressed them in newer versions.
Validated algorithms against existing prime counting methods, showing improved results.

Abstract

This paper presents the complete developmental arc of the Ashik-Wheel Segmented Sieve (AWSS), a family of high performance algorithms for counting prime numbers up to a large integer N, implemented entirely in Python. The study documents four distinct algorithmic generations, each building upon the findings—and failures—of its predecessor.

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Cite This Study

Ashik Rahim (Wed,) studied this question.

synapsesocial.com/papers/69b4fa9ab39f7826a300b4ff https://doi.org/https://doi.org/10.5281/zenodo.18968525

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