[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.