Fun With Primes

My original C and early JavaScript experiments with prime numbers, natural decomposition, and the patterns between consecutive primes.

I worked on these experiments in college, before AI coding tools were part of the process. I'm proud of this work, especially the attempt to divide a sieve's work across threads. This repository keeps the original source available to explore, including the unfinished parts.

For the later interactive browser project, see fun_with_primes. It carries forward these C sources alongside a separate JavaScript Web Worker implementation.

Start exploring

If you're curious about…	Start here
The threaded sieve	eratosthenes.c and the explanation below
Generating and printing a prime list	primeList.c
Natural-number decomposition	naturalDecomposition.c and eratosthenesFull
Gaps and patterns between primes	primeDifference.c and primeSieveDifference.c
Prime frequency over intervals	primeFrequency.c
Early browser experiments	javascript/index.html, with primality, factor, and sieve functions

How the threaded sieve works

threadPartialSieve is the worker routine for pth_eratosthenesPrime. The source header credits Vincent T. Mossman and records an update on November 5, 2016; the corresponding source history preserves that stage of the experiment.

The design divides the sieve's factor-marking passes among POSIX threads:

1. The caller initializes a shared int flag array with one entry per number from 1 through n.
2. It starts the number of workers specified by the mutable global numberOfThreads, initialized to 4 in this source. There is no automatic CPU-count detection.
3. Each worker starts at index i = rank + 1, advances by numberOfThreads while i < sqrt(n), and marks larger multiples of i + 1 as composite. The code skips later passes for even factors.
4. After joining the threads, the caller counts the remaining flags and copies their numbers into an unsigned long result array.

All workers operate on the same flag array; they do not own separate number ranges. This reduced sieve is intended to produce a prime list, while eratosthenesFull supports the separate natural-decomposition experiments.

Reading and running the originals

These are individual experiments rather than a single packaged application. Several source headers contain their original build and usage notes. For example, primeList.c documents:

gcc primeList.c -pthread -lm -o primeList
./primeList 100

That command requires a C compiler, POSIX threads, and the math library. Treat it as historical guidance rather than a guarantee for every current toolchain. Review the source before running it, start with a small input, and build locally rather than relying on the committed binaries.

The browser files live in javascript/. The HTML page loads the accompanying scripts directly and includes an external Google Fonts stylesheet.

Things to know before reuse

• The threaded sieve leaves the flag for 1 set, so its output includes 1 even though it is not prime.
• Threads can write the same flag-array entries without synchronization. Correctness and thread safety need review before reuse.
• Some experiments are unfinished and may need fixes to compile with a current toolchain.
• naturalDecomposition.c and primeFrequency.c open their corresponding .txt output files for writing, replacing existing contents.
• Timing output is part of the experiments; this repository makes no benchmark or performance guarantee.

The original source, comments, and filenames are preserved here so the work can be read in its own context.

Original project artwork