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## when are polynomials prime?

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• Message: 1 Date: Sun, 02 Apr 2006 17:11:26 -0000 From: gordon_as_number Subject: primes of polynomials If you want to prove a
Message 1 of 1 , Apr 4, 2006
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Message: 1
Date: Sun, 02 Apr 2006 17:11:26 -0000
From: "gordon_as_number" <gordon_as_number@...>
Subject: primes of polynomials

If you want to prove a polynomials P(x) is prime,
isnt enough to determine the assoiated roots.

Kermit says:

Gordon, it's an elementary theorem that a polynomial in integer coeficients

of degree M is prime in the integers provided

its value is a prime integer sufficiently often.

I don't remember at the moment whether the critical number of primes is

M+1 or 2 M or 2 M + 1.

At least I can assure you that if a polynomial of degree M with integer
coeficients takes on
2 M + 1 prime integer values, then that polynomial must be prime in the
integers.

It might be sufficient to take on M+1 values, but I don't feel sure about
that.
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