# [FOM] Prime values of polynomials

joeshipman@aol.com joeshipman at aol.com
Wed Mar 5 13:22:30 EST 2008

```That theorem concerns multivariable polynomials; I am referring to
single-variable polynomials.

-----Original Message-----
To: Foundations of Mathematics <fom at cs.nyu.edu>
Sent: Tue, 4 Mar 2008 12:52 pm
Subject: Re: [FOM] Prime values of polynomials

According to Matiyasevich's theorem, every recursively enumerable set of
natural numbers is a range of some polynomial with integer coefficients.
This means that, in particular, the set of all prime numbers can be
represented as such an image. There are explicit examples of such
polynomials, e.g., in the latest Notices of the AMS. Such polynomials
take infiitely many prime values. So, contrary to what you read, such
polynomials are well known.

-----Original Message-----
>From joeshipman at aol.com

I have read that no integer-coefficient polynomials of degree >1 are
known to take infinitely many prime values.

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