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:


 * an infinite set of numbers with greatest common divisor exceeding unity, or
 * infinitely many prime numbers.

Historical Note
Stated in 1857 by the Ukrainian mathematician Viktor Bunyakovsky.