A Prime Counting Gallery
- A Starting Point
- The Base Formula
- Stretching the Count of Primes Horizontally
- Scaling the Count of Primes Vertically
- Filtering Small Primes
- Filtering Prime Powers
- Scaling Vertically, Term by Term
- Sampling and Smoothing
- Recentering
- Recentering, Extending to Rationals
- Recentering, at Multiple Scales
- Counting with Symmetry Reduction
- Counting Variants with Symmetry Reduction
- An Alternative Prime Count
- An Additive Equivalent
- A Conclusion and Some Notes
Counting Primes
- An Introduction
- How This Core Idea Actually Works
- The Basic Approach
- Using a Wheel for Speed
- Rewriting in terms of Divisor Counts
- Refining the Wheel
- Using Symmetry Reduction for Speed
- Combining Wheel and Symmetry Reduction for Even More Speed
- A Speed Comparison
- A Survey
- A Broader Speed Comparison
- Possible Evolutions of This Approach and a Conclusion
- Wheel and Symmetry Reduction in C++
- Counting in $O(n^{\frac{2}{3} +\epsilon })$ time $O(n^{\frac{1}{3}+\epsilon})$ space in C++
Some Basics