In Theorem 1.1 (i) of http://matwbn.icm.edu.pl/ksiazki/aa/aa24/aa2451.pdf, Iwaniec showed that a certain type of quadratic formpolynomial $P(x,y)$ represents infinitely many primes, where $(x,y) \in \mathbb{Z}^2$. 
Is there any simple argument showing that $P(x,y)$ also represents infinitely many primes, where $(x,y) \in \mathbb{Z}_+^2$?
Any suggestions would be greatly appreciated. Thank you in advance.
In Theorem 1.1 (i) of http://matwbn.icm.edu.pl/ksiazki/aa/aa24/aa2451.pdf, Iwaniec showed that a certain type of quadratic form $P(x,y)$ represents infinitely many primes, where $(x,y) \in \mathbb{Z}^2$. Is there any simple argument showing that $P(x,y)$ also represents infinitely many primes, where $(x,y) \in \mathbb{Z}_+^2$?
Any suggestions would be greatly appreciated. Thank you in advance.
In Theorem 1.1 (i) of http://matwbn.icm.edu.pl/ksiazki/aa/aa24/aa2451.pdf, Iwaniec showed that a certain type of quadratic polynomial $P(x,y)$ represents infinitely many primes, where $(x,y) \in \mathbb{Z}^2$.
Is there any simple argument showing that $P(x,y)$ also represents infinitely many primes, where $(x,y) \in \mathbb{Z}_+^2$?
Any suggestions would be greatly appreciated. Thank you in advance.
