  n this paper, we state several conjectures regarding distribution of primes
and of pairs of primes represented by irreducible homogeneous polynomial in two
variables $f(a,b)$. We formulate conjectures with respect to the slope $t=b/a$
for any irreducible polynomial $f$. Here, we formulate a conjecture for all
irreducible polynomials.
  We also consider conjectures for distribution of pairs of primes. It show
unexpected relation to multiple Dedekind zeta function -
  at $s=2$ for one prime and at $(s_1,s_2)=(2,2)$ for pairs of primes. We
tested the conjecture for pairs of primes for several quadratic fields. The
conjecture for pairs of primes and multiple Dedekind zeta function over the
Gaussian integers provide error less than a tenth of a percent.
  We also tested conjectures that compare sets of primes in a pair of different
quadratic fields. Numerically, such quotients can be expressed in terms of
regulators and class numbers.
  Some of the data, together with the code, is available on GitHub, (see
\cite{Zouberou}).
