Abstract. Let Q(x; y) be a primitive positive definite quadratic form with
integer coecients. Then, for all (s; t) 2 R2 there exist (m; n) 2 Z2 such that
Q(m; n) is prime and
Q(m- s; n - t) Q(s; t)0:53 + 1:
This is deduced from another result giving an estimate for the number of prime
ideals in an ideal class of an imaginary quadratic number eld that fall in a
given sector and whose norm lies in a short interval