josh_kratz

3 ms·

1. 1.▲
   by josh_kratz 1y ago

   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
2. 2.▲
   by josh_kratz 1y ago

   Yep, that’s the one. Nothing crazy. It might get angry at certain versions of .NET though.
3. 3.▲
   by josh_kratz 1y ago

   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,
4. 4.▲
   by josh_kratz 1y ago

   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 quadrilli
5. 5.▲
   Trillion-Scale Goldbach Verification on Consumer Hardware -novel Algorithm [pdf](zenodo.org)

   7 points by josh_kratz 1y ago|9 comments
6. 6.▲
   by josh_kratz 1y ago

   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.