# Schinzel's hypothesis H

From Number

## Statement

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

### Weaker facts

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 |