Is $d^2+d+1$ prime for infinitely many $d\in \mathbb{Z}\_{>0}$?


This is expected by the [Bunyakovsky conjecture](https://en.wikipedia.org/wiki/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 $p(x) = x^2+x+1$?



Primes of the form $d^2+d+1$
To answer the question and summarizing the comments: the answer is no, there is no known proof of this conjecture.


