Most of my books ask why factoring is hard. Lumens Per Watt was my attempt to test that directly: could I evolve a better factoring method, and if not, where exactly does it stop improving?
The idea
Think of the number line as a dark room and an algorithm as a lamp. A good lamp lights up a lot of the room for very little power. So I scored every candidate algorithm the way you’d score a light bulb, by illumination per watt: how much of the number line it settles, divided by the total energy it burned, all on one CPU so the comparison stayed fair. Then I mutated the best lamps, measured them again, and kept the winners.
Keeping myself honest
Experiments like this are easy to fool yourself with, so I built in checks. Each run had a sealed judge that the evolving code couldn’t see. Before runs, I sent status updates to outside AI reviewers for forecasts that stayed sealed until the results were in. Some of those forecasts failed, and that’s recorded too.
What happened
The search did find real improvements, but they were the kind you can name. Left to evolve, it rediscovered a known classic, Pollard’s rho method. Some early gains turned out to be padding in the score rather than real speed, and the advantage on held-out numbers shrank as the measurement got stricter. That’s an honest result: a better lamp, but no new kind of light. I paused the project after its first phase and left notes in the repository so anyone can pick it up.
The story is told in full in The Big Book of Prime Secrets and Light Through the Holes. It also has songs, “Lumens Per Watt” and “Ten Times, Not a Hundred”, with their own music videos.
Code and notes: github.com/onojk/lumens-per-watt
