Recently I was studying a particular problem and I was faced with the following question: Is $d^2+d+1$ prime for infinitely many $d\in \mathbb{Z}_{>0}$?

This is expected by the Bunyakovsky conjecture which says that, under some conditions, given a polynomial $p(x) \in \mathbb{Z}[x]$ we have $p(d)$ prime for infinitely many $d\in \mathbb{Z}_{>0}$. Is there some proof of this when $p(x) = x^2+x+1$?