Re: CVS commit: src/games/factor

[der Mouse <mouse%Rodents-Montreal.ORG@localhost>]

> connect(): No such file or directory

...um?

>>>> Aleksej, Joerg is correct by definition.  [...]
>>> Kristaps, Joerg is incorrect by definition.  [...]
>> From "An Introduction to the Theory of Numbers", [...]
> I asked explicitly to avoid mere proclamations and provide rationale
> behind accepted definitions.

Why is it up to us to provide you with remedial education in number
theory?

The real reason for defining "prime" in a way that excludes 0 and 1 is
that it is convenient.  There are many theorems that, under the
currently widespread definiton, can speak of "any prime", whereas, with
a definition that includes 0 and 1, would have to instead say something
more like "any prime except 0 or 1".  In contrast, there are few-to-no
results that would be simplified, that currently read "0 or 1 or a
prime" but which could under your alternative definition could instead
read simply "a prime".

You can use the five-letter sequence "prime" to mean anything you
please.  However, for widespread use - and I think the factor(6) man
page counts - I believe NetBSD should stick to widely accepted
definitions, and those exclude 0 and 1.  (If you wish to commuicate
usefully with others, you may wish to consider using the widely used
meaning yourself.)

Of course, factor(6) does not necessarily have to factor a number into
"prime"s by this definition.  However, given common mathematical use of
"factor" as applied to integers, this is probably the least
mathematically surprising way for it to operate.  For many purposes, it
is also the most useful; while there may be reasonable debate as to the
extent to which "useful" aligns with "mathematically expected", that is
not the debate I've seen happening here - or, rather, it's not the one
which has recently been generating much heat and little light; I did
see it happen, and mostly get resolved, before the thread veered off
onto this tanget.

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