4
$\begingroup$

Has there been any progress on the Bouniakowsky conjecture? In particular, has anyone been able to prove something for a particular polynomial - or for a class of them?

(I can't seem to find anything, but that could be due to the fact that there seem to be many ways of spelling Bouniakowsky.)

Improve this question
$\endgroup$
2
  • 1
    $\begingroup$ No. It's still not known for a single polynomial of degree at least two. If it gets proved, you'll hear of it. $\endgroup$
    – Felipe Voloch
    May 30, 2012 at 23:41
  • $\begingroup$ @KConrad: that was a silly typo. Thanks. $\endgroup$
    – Joshua Seaton
    May 31, 2012 at 0:38

1 Answer 1

Reset to default
8
$\begingroup$

It now goes by the name "Schinzel's Hypothesis H", which has a Wikipedia entry. A quantitative form is known as the "Bateman-Horn Conjecture", which also has a Wikipedia entry.

Short answer: no progress, but better conjectures!

Improve this answer
$\endgroup$
3
  • $\begingroup$ I figured as much. Thank you, Kevin. $\endgroup$
    – Joshua Seaton
    May 31, 2012 at 0:39
  • 2
    $\begingroup$ Isn't H much more general than Bouniakowsky? Doesn't it deal with finite collections of polynomials, while Bouniakowsky just deals with a single polynomial? $\endgroup$
    – Gerry Myerson
    May 31, 2012 at 7:10
  • $\begingroup$ @gerry: That's right, that's part of the "better" to which I referred. In the single polynomial situation, I think it is common to write "by Schinzel's Hyp. H, ...", while I'd never heard of Bouniakowsky's Conjecture before. $\endgroup$
    – Kevin O'Bryant
    May 31, 2012 at 15:03

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.