# Tag Info

## Hot answers tagged provability

Accepted

### Is there any conjecture that has been proved to be solvable/provable but whose direct solution/proof is not yet known?

It is known that there is an even integer $n\le246$ such that there are infinitely many primes $p$ such that the next prime is $p+n$, but there is no specific $n$ which has been proved to work (...
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Accepted

### Is there any conjecture that we know is provable/disprovable but we haven't found a proof of yet?

There are plenty of problems in mathematics which can be done by a finite computation in principle, but for which the computation is too large to actually carry out and we don't know of any shortcut ...
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### Is there any conjecture that we know is provable/disprovable but we haven't found a proof of yet?

Eric Wofsey's answer is certainly more comprehensive, but I thought I'd provide an example where the assurance that there's a proof of $P$ or $\neg P$ that's not of the form "there's a straightforward,...
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### Is there any conjecture that has been proved to be solvable/provable but whose direct solution/proof is not yet known?

I am not sure this answers your question but it seems to come close. The Wikipedia article Skewes number states In number theory, Skewes's number is any of several extremely large numbers used by ...
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### Is there any conjecture that has been proved to be solvable/provable but whose direct solution/proof is not yet known?

It's known that no matter the size of the board, the first player has a winning strategy in Chomp, but an explicit winning strategy is only known for smallish boards.
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### How long can proofs be?

This function grows really fast: there is no computable function which bounds it! To see this, note that if we had a computable bound on $f$ we could tell whether a sentence $\sigma$ is consistent ...
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### I don't understand Gödel's incompleteness theorem anymore

This answer only addresses the second part of your question, but you asked many questions so hopefully it's okay. First, there is in the comments a statement: "If Goldbach is unprovable in PA ...
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### Were there any proofs of whether or not a statement could be proved true or false before Gödel's Incompleteness Theorems?

Does proving the parallel postulate is not provable from the other Euclidean postulates count? That proof dates back to Lobachevsky and Gauss and one of the Bolyai's.
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### Semantics for minimal logic

Yes, tweaking Kripke semantics based on that for intuitionistic logic does the trick. If I recall right, there are slightly different ways of doing this. Here's a version for minimal logic and some ...
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