Schinzel–Sierpiński hypothesis H

Let $m\in\mathbb{N}$ and let $f_1,\ldots,f_m\in\mathbb{Z}[x]$ be polynomials. Suppose that there is no prime number $p$ such that

$$p\mid\prod_{i=1}^m f_i(n)$$

for every $n\in\mathbb{N}$. Schinzel–Sierpiński hypothesis H. There are infinitely many $n\in\mathbb{N}$ such that $f_1(n),\ldots,f_m(n)$ are all prime simultaneously. This is the standard prime-values conjecture for a finite family of polynomials; it is a generalization of the corresponding one-polynomial conjecture and remains open in general.