# Dickson's conjecture

From Number

## Statement

Suppose are integers with all the . Then, consider the polynomials:

Then, one of the following is true:

- There is a prime number such that the product is times an integer-valued polynomial. In other words, one of the polynomials is always congruent to 1 modulo .
- There exist infinitely many [[natural number]s for which
*all*the values are*simultaneously*prime.