1. The number of prime solutions to the equation $x y + 41 z = 2009$ is ( ) groups.
(A) 4
(B) 6
(C) 8
(D) 10
- 1.A.

From the original equation, we get
$$
x y=2009-41 z=41(49-z) \text {. }
$$

Since $x, y$ are prime numbers, then $x=41$ or $y=41$.
(1) When $x=41$, $y=49-z$, it follows that $y$ or $z$ must be even, hence $(y, z)=(2,47),(47,2)$, at this point, the original equation has two sets of prime solutions;
(2) When $y=41$, similarly to (1), the original equation also has two sets of prime solutions.