[seqfan] Re: A174397 and primes with negative value.
Charles Greathouse
charles.greathouse at case.edu
Fri Mar 19 19:13:18 CET 2010
Agreed. In the OEIS, and in fact in most places, primes are assumed
to be positive. But -2 etc. are prime elements of Z (and hence an
irreducible elements of Z -- though since Z is a UFD, they're the
same).
Charles Greathouse
Analyst/Programmer
Case Western Reserve University
On Fri, Mar 19, 2010 at 1:27 PM, Jonathan Post <jvospost3 at gmail.com> wrote:
> "A prime number (or prime integer, often simply called a "prime" for
> short) is a positive integer p>1 that has no positive integer divisors
> other than 1 and p itself. (More concisely, a prime number p is a
> positive integer having exactly one positive divisor other than
> 1.)..."
> http://mathworld.wolfram.com/PrimeNumber.html
>
> I can see that -2 is a prime in Z, as it is only divisible by itself,
> the unit -1, and the positive prime 2. But that requires tweaking the
> initial definition to substitute "unit" for "1."
>
> On Fri, Mar 19, 2010 at 10:16 AM, Richard Mathar
> <mathar at strw.leidenuniv.nl> wrote:
>>
>> V. Orlovsky is defending his definition in A174397 (with negative numbers,
>> obviously) with a link to http://primes.utm.edu/notes/faq/negative_primes.html
>> arguing that primes can be negative numbers, so the mention of absolute
>> values in the definition is not needed. I cannot make friend with that idea.
>> Is there a general consensus (at least within the OEIS) that primes are >=2 ?
>>
>> Richard Mathar
>>
>>
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