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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:

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What does “unconfirmed or conditional” mean on this page and what is the difference between results $H=12006$ and $H=5414?$

Zev Chonoles
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curiousamateur
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    unconfirmed, conditional – Chris Eagle Jul 08 '13 at 19:11
  • Those results identified in this way have a higher likelihood of being found incorrect. – vadim123 Jul 08 '13 at 19:13
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    The way the project is using these terms, an argument is unconfirmed until a person other than its originator verifies its correctness. Conditional means either that its truth depends on the validity of an argument the details of which at the moment have not been completely worked out, or that it depends on computations eventually confirming some theoretical bound. At the pace progress has been happening, confirmation tends to happen a couple of days after arguments are posted. And computations are now in a range that I do not expect the second meaning of conditional to come into play again. – Andrés E. Caicedo Jul 08 '13 at 19:25
  • Note that the argument is sufficiently long that sometimes it may take a short while to see what pieces still need confirmation. Tao's latest entry on his blog, and some of the pages in the wiki help enourmously to keep track of these pieces. – Andrés E. Caicedo Jul 08 '13 at 19:30
  • (See here and Tao's reply.) – Andrés E. Caicedo Jul 11 '13 at 05:26
  • The $720; 5414$ estimate has now been confirmed – Mark Bennet Jul 22 '13 at 21:09

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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.

Mark Bennet
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Uncofirmed likely means that the result (likely based on lengthy computer calculations) has not been counter-checked enough by other researchers (e.g. using a different computer program).

Conditional means that the result depends on some as of yet unproven assumption, in this context of prime numbers the most ubiquitious candidate for such a condition is the Riemann hypothesis.

Hagen von Eitzen
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