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.

Source of Name

This entry was named for Viktor Yakovlevich Bunyakovsky.

Historical Note

The Bunyakovsky Conjecture was first stated in $1857$, by Viktor Yakovlevich Bunyakovsky.