The following paper provides result on an analog of twin primes conjecture for $\Bbb F\_q[X]$
<http://pollack.uga.edu/twins.pdf>


Is there an analog of twin primes conjecture for $\Bbb Z[X]$?


An analog similar to that in the paper of the form "Given $g(X)\in\Bbb Z[X]$, $\forall i\in \Bbb N,\mbox{ }\exists f\_i(X)\in\Bbb Z[X]$ with $\operatorname{deg}(f\_i)>\operatorname{deg}(g)$ and $\forall i,j\in\Bbb N$, $i\neq j\implies f\_i(X)\neq f\_j(X)$ such that $f\_i(X),f\_i(X)+g(X)$ are both irreducible in $\Bbb Z[X]$".



Twin primes for polynomials in $\Bbb Z[X]$
Use the Chinese remainder theorem to construct infinitely many $f\_i$ such that $f\_i$ is Eisenstein at one prime, and $f\_i+g$ is Eisenstein at another.


