Schinzel's hypothesis H
Suppose are all irreducible polynomials with integer coefficients and with positive leading coefficient, such that the product does not have any fixed divisors, i.e., it cannot be expressed as a proper multiple of an integer-valued polynomial. Schinzel's hypothesis H states that there are infinitely many natural numbers satisfying the condition that are all simultaneously prime.
Related facts and conjectures
|Fact or conjecture||Status||How it fits with Schinzel's hypothesis H|
|Bunyakovsky conjecture||open||We are dealing with only one irreducible polynomial of degree two or higher|
|Dirichlet's theorem on primes in arithmetic progressions||proved||We are dealing with one irreducible polynomial of degree one|
|Twin prime conjecture||open||We are dealing with the irreducible polynomials and|