This technical deep dive explores C implementations for generating all 32-bit prime numbers, targeting Linux systems. The goal is to create a binary file containing every prime up to 4,294,967,295, with each prime stored as 4 little-endian bytes. The article benchmarks multiple approaches, with the basic trial division implementation taking approximately 24 minutes and 20 seconds of user time on the author's system.

Trial division serves as the foundation, checking divisibility by all primes up to the square root of each candidate number. The implementation uses a growing array of discovered primes, starting with {2} and testing odd numbers sequentially. Wheel factorization optimization, which eliminates obvious non-primes based on modular arithmetic patterns, provides minimal improvement—reducing runtime to about 23 minutes and 30 seconds when using a wheel based on the first five primes.

The article includes complete C code for both approaches, performance analysis, and verification through SHA-256 checksums. The target output file should begin with the byte sequence 02 00 00 00 03 00 00 00 05 00 00 00 07 00 00 00 and have a final hash of 272eb05aa040ba1cf37d94717998cbbae53cd669093c9fa4eb8a584295156e15.