  We investigate the average distribution of primes represented by positive
definite integral binary quadratic forms, the average being taken over negative
fundamental discriminants in long ranges. In particular, we prove corresponding
results of Bombieri-Vinogradov type and of Barban-Davenport-Halberstam type,
although with shorter ranges than in the original theorems for primes in
arithmetic progressions: The results imply that, for all $a>0$, the least prime
that can be represented by any given positive definite binary quadratic form of
discriminant $q$ is smaller than $|q|^{7+a}$ for all forms to "most"
discriminants; moreover, it is even smaller than $|q|^{3+a}$ for "most" forms
to "most" discriminants.
