[seqfan] Re: A174397 and primes with negative value.

William Keith wjk26 at drexel.edu
Fri Mar 19 21:45:23 CET 2010

 Richard Mathar 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

I would not agree with that.  Negative primes are primes in Z by the common algebraic definition.  They are not primes in N, because they are not in N.  Whether a given sequence "should" consider negative primes, or values in general,  is going to be dependent on the context of utility for that sequence, and values of an indefinite form are going to range both positive and negative, so I'm quite comfortable with signs here.  A good example would be the flip sequence n^3 + (n+1)^3 - (n+2)^3, which starts with negative values but eventually turns positive.

William Keith

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