[seqfan] Re: -5 is not a prime

[M. F. Hasler]

We have two words, "irreducible" and "prime". It makes sense to use the
second for unique representatives of the equivalence classes of the first,
modulo the group of units. In particular when a very natural choice exists,
like in the case of an ordered ring like *Z* (where we can take the primes
to be the positive irreducibles) or for polynomials over fields where we
can take the representative with leading coefficient 1.

Indeed the different CAS use different conventions for "negative primes".
If I remember well, some will even say isprime( -2 ) = false (or even throw
an error for non-positive arguments) and at the same time say
ispseudoprime( -2 ) = true.
If I remember well, Mathematica's primeQ function actually does not test
primality but pseudo-primality.

- Maximilian

On Sun, 3 Jan 2021, 15:00 William Keith, <william.keith at gmail.com> wrote:

> Unique factorization is a property that is defined up to multiplication by
> units.  5 and -5 are associates; both are prime.  Both generate the same
> prime ideal in the integers.
>
> Best,
> William
>
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