[ruby-core:22700] Re: [Bug #1243] 1 is prime

On Wed, Mar 4, 2009 at 9:15 AM, Yugui (Yuki Sonoda) <[e-mail]> wrote:
> On 3/4/09 1:40 AM, Dave B wrote:
>> + 炯alue = -value if value < 0 --- NOT required ?
>> + 灑eturn false if value < 2
>>
>> I think your negative guard is not required?
>
> For a arbitrary positive prime number p, -p is a prime element in the
> ring of integers. On the other hand, it is sure that just saying "prime
> numbers" means positive ones.
>
> (http://en.wikipedia.org/wiki/Prime_number)
>> Without further specification, however, 菟rime numberalways means a
> positive integer prime
>
> I am at a loss whether -2.prime? should return true or false? hich is
> more useful for Rubyists?
>
IIRC 1 was discarded as prime because it messed up the uniqueness of
factorization. If we want to keep this spirit I see no solution for
negative numbers.
One could maybe define that all negative numbers are composed with the
exception of -1, which is prime ARRRGH and the additional rule that -1
can only occur ? times (in the regexp sense of ? ) in a factorization.
But maybe it makes more sense to say x.prime? if and only if x.abs.prime?
and
for all x: x.primefactors.count{ | f| f.negative? } < 2

I guess these are lousy ideas, does anyone have something better to suggest?

Cheers
Robert

> --
> Yugui <[e-mail]>
> http://yugui.jp
>
>



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