What does “unconfirmed or conditional” mean on this site? On the home page of the “Bounded gaps between primes” polymath project, there are listed bounds for $H$ in Zhang's proof of prime gaps. For example: > !enter image description here What does “unconfirmed or conditional” mean on this page and what is the difference between results $H=12006$ and $H=5414?$

I think "unconfirmed" means - "someone has produced an argument for this, but it hasn't been rigorously checked yet."

I think "conditional" means - "this estimate is based on some other assumption we think we can prove, but we haven't filled in all the details yet."

Both are rough translations. By far the best source for the detailed (a word I use advisedly) arguments is Terry Tao's excellent blog. As I write, it seems likely that many of the $?$ estimates will shortly be confirmed, as the arguments have now been completed and checked.