# Talk:Bateman–Horn conjecture

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Field:  Number theory

What's all this about Bunyakovsky's property? Charles Matthews 18:56, 27 August 2006 (UTC)

Right, it is covered by the discussion of fixed prime divisors at Schinzel's hypothesis H. Since that comes up on both pages, perhaps it could be wiith advantage moved to integer-valued polynomial. Charles Matthews 19:00, 27 August 2006 (UTC)

## Is there a formulation for Subsets?

I'd like an approximate number of simultaneous solutions of 7 out of the first 8,9,10,11,12 of a sequence of polynomials being prime. Is there a formulation in the literature of an expansion of the Bateman-Horn conjecture to cover this question and should it be included in the article if it does exist? For me, the question is apropos of the sequence {x2n+xn-1} applied to n=1,2,..., where the situation is that 10 is the only known x such that seven of the first nine n are prime, nine in fact being (right now) replaceable by up to twelve.Julzes (talk) 01:17, 21 October 2009 (UTC)

An example is now known for 7 out of 10, the polynomial given being prime for n=1 through 6 for the first time with the value x=610357585, where n=10 also gives a prime.Julzes (talk) 05:11, 22 October 2009 (UTC)

You could use inclusion-exclusion on Bateman-Horn to count the number of (conjectured, asymptotic) solutions. CRGreathouse (t | c) 14:35, 9 February 2010 (UTC)

## Error

There is an error in the final forumula: on the LHS, the argument is "x", on the right it is "n". I suppose, some one mixed them up? 131.130.16.17 (talk) 13:30, 21 May 2010 (UTC)

## Results

What are the known results when prime values are replaced with almost-prime values? —Preceding unsigned comment added by Barylior (talkcontribs) 21:53, 21 July 2010 (UTC)