Schinzel's hypothesis H

Named after Andrzej Schinzel.

Schinzel's hypothesis H

1. (number theory) A famous open problem in mathematics, the hypothesis stating that, for every finite collection ${\displaystyle \{f_{1},f_{2},\ldots ,f_{k}\}}$ of non-constant irreducible polynomials over the integers with positive leading coefficients, one of the following conditions holds: (i) there are infinitely many positive integers ${\displaystyle n}$ such that all of ${\displaystyle f_{1}(n),f_{2}(n),\ldots ,f_{k}(n)}$ are simultaneously prime numbers, or (ii) there is an integer ${\displaystyle m>1}$ (called a fixed divisor) which always divides the product ${\displaystyle f_{1}(n)f_{2}(n)\cdots f_{k}(n)}$.