A Prime Counting Gallery
  • A Starting Point
  • Stretching the Count of Primes Horizontally
  • Scaling the Count of Primes Vertically
  • Filtering Small Primes
  • Filtering Prime Powers
  • Scaling Vertically, Term by Term
  • A Conclusion and Some Notes
A Prime Counting Gallery 2:
Approximation and Extensions
  • 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
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