[throwaway150]

I truly hate to bring this up, knowing how much passion has gone into this project. But there's an important thread got buried due to arguments! That thread raises serious concerns about the validity of this bold claim.

As highlighted by @tromp and @oefrha (https://news.ycombinator.com/item?id=43734877) it is clear, clients can cheat. So we can't be 100% sure that none of the clients cheated. What if a counterexample to the conjecture exists, but a dishonest client simply failed to report it? Math results require rigor and without rigor no claim can be trusted. Without rigor, this bold assertion remains just that. A claim, not a fact.

OP! On top of that, you're being evasive in threads where you're being asked how your validation works and you went so far as to flag a pertinent thread. That definitely doesn't inspire confidence. Addressing the validation questions is absolutely 100% necessary if you want this to be seen as more than just a claim.

[eddd-ddde]

Even if all clients are truthful and 100% correct, the lack of counter examples would still be essentially meaningless, right?

[pavel_lishin]

It doesn't even have to be dishonesty; it could be a poorly timed cosmic ray flipping a bit.

[GTP]

Yes, and I think this is actually more likely than someone intentionally modifying the code and finding a counterexample. Related, I'm now wondering what would happen if someone sent in a fake result claiming to have found a counterexample: will the website report the conjecture as proven false? It wouldn't last more than a few hours on the website, but I can totally see someone doing it as a prank.

[akoboldfrying]

Well, in the worst case, such a false positive can be discovered in at most the same amount of time as a typical block takes, by rerunning that same entire block in the server. And since we expect positives (false or otherwise) to occur very rarely, this should not be expensive.

Except... Doing this level of verification would enable DoSing the server very easily -- just send lots of false positives.

[GTP]

Yes, checking a specific false positive would be trivial and extremely fast[0], as it's just about summing two numbers. But, if the server doesn't do the check, having the site report a counterexample to Goldbach's conjecture would be an easy prank to pull off.

[0] Verifying that those two numbers are actually primes may take more time, but it seems to me that we're still dealing with number sizes for which primality testing isn't that hard. After all, the code here seems to just be using Erathostene's sieve to find primes.