[josh_kratz]

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.

[SethTro]

> Goldbach states: every even number ≥ 4 is a sum of two primes. The naive check for an even n tries many primes p and hopes that n − p is prime. Our idea is simpler: fix a small set of primes Q = {q1, . . . , qK} (the “gear”), and for each even n only test p = n − q with q ∈ Q

I don't see how your idea is different from the naive check. As far as I can tell you are basically saying do the naive check but only up to p > 250-300?

[josh_kratz]

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.

[SethTro]

I don't see any benchmarks on your github.

How long does it take for you to test up to 10^9? 10^12?

[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.