Bunyakovsky conjecture

The Bunyakovsky conjecture (or Bouniakowsky conjecture) stated in 1857 by the Russian mathematician Viktor Bunyakovsky, asserts when a polynomial ${\displaystyle f(x)}$ in one variable with positive degree and integer coefficients should have infinitely many prime values for positive integer inputs. Three necessary conditions are

Bunyakovsky's conjecture is that these three conditions are sufficient: if ${\displaystyle f(x)}$ satisfies the three conditions then ${\displaystyle f(n)}$ is prime for infinitely many positive integers ${\displaystyle n}$.

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