We introduce today a new feature of Programming Praxis: essays. An essay isn’t an exercise; it doesn’t present a task for you to perform, but instead provides extended discussion and complete source code. Though essays may be based on exercises, the idea is that an essay can delve more deeply into a topic than is possible in the limited space and time of an exercise.

Our first essay is about a topic dear to my heart: programming with prime numbers. The essay presents two versions of the Sieve of Eratosthenes, uses trial division to identify primes and factor composites, and provides the Miller-Rabin pseudoprime checker and Pollard rho factoring algorithm. Source code is given in five languages: C, Haskell, Java, Python, and Scheme.

Please read the essay, and feel free to comment on it below; comments on the essay itself are closed. Let me know if you see any errors. And feel free to link to the essay on the internet if you know of places where it is appropriate.