Talk:Schinzel's hypothesis H

message: I have read references to a so-called "Schinzel's Conjecture" that says there is always a prime between x and x+ln(x)^2, whenever x>=8.  Is this a consequence of Schinzel's hypothesis H?  If so, can this article be updated to state (and explain) this.  If not, can the article be updated to point out that there are other so-called Schinzel conjectures besides this one?  Thanks! —GraemeMcRaetalk 22:09, 29 December 2007 (UTC)
replies: text: It's always possible to edit.  If you have a source, go right ahead.  I note that you are around periodically, though nobody answered you here.  One point is that this does have a specific title.  It might be better actually to take Schinzel's name off of it and do a re-direct to this article, simply making it clear at the outset that Hypothesis H is Schinzel's.  I see no way to get from this hypothesis to the one you give since this deals with arbitrarily large numbers while yours deals with specific bounds.  Definitely No.  One reason the article is titled as it now stands may be that the one you give, for instance, is named Schinzel's hypothesis [insert letter].  There may be some other hypotheses of his, like the one you state, that deserve their own entries, and I expect that the article on Schinzel deals with what could be expanded upon by wikipedians.Julzes (talk) 00:27, 21 October 2009 (UTC)

text: This is related to Cramér's conjecture (a term sometimes used about variations of what that article says). I have not heard about Schinzel in this context. PrimeHunter (talk) 00:53, 21 October 2009 (UTC)
thread_title:  Hey mathematicians!  What about Schinzel's Conjecture about prime gaps? 

message: This article deals with a conjecture that many believe true while many also believe it to be false.  This is rather rare in mathematics, with most conjectures either established, refuted, supported or undermined in reasonable time.  It seems this is one of those where one can easily waffle, but I'm not an expert.  I'm wondering about what experts have said and whether that ought not be placed in the article along with whatever (little?) justification they may give.Julzes (talk) 00:32, 21 October 2009 (UTC)
replies: text: Is it really that "controversial"? Peter Sarnak in this recent PDF is working at a mega-conjecture that takes it into higher dimensions. I thought Hypothesis H was really what people expected to be true on standard heuristics. Charles Matthews (talk) 07:09, 21 October 2009 (UTC)
thread_title:  Is anybody around who can give Quality Opinions 

message: I felt that the last sentence on a global obstruction might better reflect that the hypothesis is so far only conjectural, so I modified the sentence with 'assuming that hypothesis H is in fact correct'.  Being what I think is a minor change, I did it prior to any debate.  —Preceding unsigned comment added by Julzes (talk • contribs) 21:40, 25 October 2009 (UTC)
thread_title:  Minor change of last sentence 

message: It might be helpful to reference Bateman-Horn conjecture, which is a quantitative form of this type of discussion. Charles Matthews (talk) 22:56, 25 October 2009 (UTC)
replies: text: Already in the article.  That's how I found it.Julzes (talk) 23:15, 25 October 2009 (UTC)
thread_title: Even broader

message: Substituted at 02:35, 5 May 2016 (UTC)
thread_title: Assessment comment

message: : Can you explain why you are not okay with the infobox here? It packages the logical connections from the "Statement" section (which should really be elsewhere) and the date of origin for the conjecture that's given in "External links". It also really doesn't take away any space from someone who chooses to ignore it. — MarkH21 (talk) 05:28, 24 February 2019 (UTC)
replies: text: I've nominated the infobox for deletion; probably best to suspend discussion here unless and until that outcome is a keep.  –Deacon Vorbis (carbon • videos) 05:31, 24 February 2019 (UTC)
thread_title:  Infobox mathematical statement 

message: The section Statement begins as follows:
"The hypothesis claims that for every finite collection \{f_1,f_2,\ldots,f_k\} of nonconstant irreducible polynomials over the integers with positive leading coefficients, one of the following conditions holds:
# There are infinitely many positive integers n such that all of f_1(n),f_2(n),\ldots,f_k(n) are simultaneously prime numbers, or
# There is an integer m>1 (called a fixed divisor) which always divides the product f_1(n)f_2(n)\cdots f_k(n). (Or, equivalently: There exists a prime p such that for every n there is an i such that p divides f_i(n).)"
In mathematics there is a huge distinction between "one of the following two conditions" and "only one of the following conditions".
If the Schinzel hypothesis is that only one of the two conditions holds, then it is necessary to say so in the article.
Otherwise this article doesn't even describe its subject correctly. 2601:200:C000:1A0:DD41:F29D:81CE:BF6E (talk) 17:47, 3 September 2022 (UTC)
thread_title:  Is it "one" or "only one" of the following conditions?