Schinzel’s Hypothesis H
Let a set of irreducible polynomials with integer coefficients have the property that for any prime there exists some such that . Schinzel’s Hypothesis H that there are infinitely many values of for which and are all prime numbers
.
The 1st condition is necessary since if is reducible then cannot be prime except in the finite number of cases where all but one of its factors are equal to 1 or -1. The second condition is necessary as otherwise there will always be at least 1 of the divisible by ; and thus not all of the are prime except in the finite number of cases where one of the is equal to .
It includes several other conjectures, such as the twin prime conjecture.
Title | Schinzel’s Hypothesis H |
---|---|
Canonical name | SchinzelsHypothesisH |
Date of creation | 2013-03-22 15:11:43 |
Last modified on | 2013-03-22 15:11:43 |
Owner | jtolliver (9126) |
Last modified by | jtolliver (9126) |
Numerical id | 5 |
Author | jtolliver (9126) |
Entry type | Conjecture |
Classification | msc 11N32 |