Question concerning A092749.

[Pieter Moree]

Labos wrote:

> See also Rivera polynomial in A090110.
> All irreducible polynomial are candidates for prime-chains or
> records.
No, that is certainly not true. They should have a large
Hardy-Littlewood constant.

What you want for a given f(x) in order to get many primes is
to exclude that f(x)=0(mod q) has a solution for small primes
q. This is the idea behind the Euler polynomial, Beeger polynomial
etc..

For a quadratic polynomial this leads one to require that the
Legendre symbol of the discriminant, D, over q should be -1 for
many consecutive q.
This has as consequence that L(1,\chi) with
chi(n)=(D/n)  will be small and
so also the class number of the associated quadratic field...
Hence the connection with the class number one problem is not
so surprising.