Bunyakovsky Conjecture

Conjecture
Let $P$ be an irreducible polynomial of degree two or higher whose coefficients are all integers.

Then, for arguments which are all natural numbers, $P$ generates either:


 * $(1):\quad$ an infinite set of numbers with greatest common divisor exceeding $1$

or:
 * $(2):\quad$ infinitely many prime numbers.

He first stated it in $1857$.