  Intersective polynomials are polynomials in $\Z[x]$ having roots every
modulus. For example, $P_1(n)=n^2$ and $P_2(n)=n^2-1$ are intersective
polynomials, but $P_3(n)=n^2+1$ is not. The purpose of this note is to deduce,
using results of Green-Tao \cite{gt-chen} and Lucier \cite{lucier}, that for
any intersective polynomial $h$, inside any subset of positive relative density
of the primes, we can find distinct primes $p_1, p_2$ such that $p_1-p_2=h(n)$
for some integer $n$. Such a conclusion also holds in the Chen primes (where by
a Chen prime we mean a prime number $p$ such that $p+2$ is the product of at
most 2 primes).

Number Theory;Combinatorics