josh_kratz

So at 12 threads. I can do 10^12 in about 3hrs and 45 mins. But obviously takes over the whole system. I think it could even be more optimized if the concept was taken further in the right hands or hardware. I should add some benchmarks for sure. Will do so soon.

Yep, that’s the one. Nothing crazy. It might get angry at certain versions of .NET though.

Think of it like this: “naive 300“ would try and check if n minus any of the first 300 primes lands on another prime. For big n, it falls apart fast as prime gaps explode, and you start missing left and right. But here I am doing a small, constant set of primes, call it the “gear”… and for each even n, I check n – q for every q in that gear. Not just as a casual test, but as a full-blown, multi-threaded, checkpointed sweep with audited logs.

The idea is that a fixed gear approach means that instead of exhaustively checking against everything, a small subset of primes (k=300) actually is sufficient for effectively complete coverage and holds true at large slices in the quadrillions, or even higher, or all the way through an entire cycle of evens to 1 trillion. It’s saving a massive amount of compute and appears to be just as effective as naive checks. Like orders of magnitude faster.

As far as I know, no one has tested this method or written an algorithm precisely like this. And then determined that k=300 is the sweet spot for primes sets. Complexity isn’t required for improvements.

Author here. This is my first published paper - developed independently. Novel approach uses a fixed set of witness primes to reduce verification to O(1) per even. Full C# implementation on GitHub for anyone to run.