Trillion-Scale Goldbach Verification on Consumer Hardware -Novel Algorithm [pdf]
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Number TheoryAlgorithm DesignComputational Mathematics
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Number Theory
Algorithm Design
Computational Mathematics
Researchers present a novel algorithm for verifying Goldbach's conjecture on a trillion-scale, achievable on consumer hardware, sparking discussion on its implications and potential applications.
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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?
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.
How long does it take for you to test up to 10^9? 10^12?
I wrote https://github.com/sethtroisi/goldbach in the last four hours and I think it's 10-100x faster than your code
I know of at least another 4x I could improve it but I've been nerd sniped enough for the night.I wouldn't trust it 100% but it finds all terms in https://oeis.org/A025018 and https://oeis.org/A025019 and I can verify in https://sweet.ua.pt/tos/goldbach.html