---- Original message ---- >Date: Sat, 04 Mar 2006 00:19:33 +0100 >From: Jean-Sibastien Bour <[EMAIL PROTECTED]> >Subject: Re: what is next? 3.10 or 4.0??? >To: misc@openbsd.org > >Reid Nichol a icrit : >> --- Jean-So?=bastien Bour <[EMAIL PROTECTED]> wrote: >> >>> Matthias Kilian a icrit : >>> >>>> a) 4 is the first non-prime, at least according to factor(6). >>>> >>>> >>> No, it is 1 :) >>> Explanation : a prime number can only be divided by two different >>> numbers : 1 and itself. 1 can only be divided by one number, >>> therefore it is not prime. >>> >> >> Wrong. >> >> You got the definition of what a prime number is wrong. A prime number >> is defined as a positive integer greater than one which has positive >> divisors 1 and itself, only. >> >> Please note that using your definition 7 is not prime because -7, -1, 1 >> and 7 all divide 7. >> >> I suggest at least looking into elementary number theory before making >> such statements again. >> Tired of spam? Yahoo! Mail has the best spam protection around >> http://mail.yahoo.com >> >> >> >No no not wrong, indeed I didn't talk about being positive. But being >prime is being positive (should have said it I agree) and have EXACTLY >TWO different divisors. And if 1 were prime you wouldn't have only one >unique decomposition in prime numbers ;) (for exemple, is 45 = 3x3x5 or >1x3x3x5 or 1x1x1x3x3x5 or... ?) It would crush many things down about >arithmetics.
nobody here is arguing that 1 IS prime. more transparently, the ideal generated by (1) is NOT a prime ideal (it's the whole ring). also, a factorization in a UFD is only unique up to multiplication by a unit. i think 1 is a unit, i'm not sure... :P > >Luckily I have learnt some things during my two year special scientific >studies (heard about "Classes priparatoires" in France ?) and this is >one of those. > i assume you also learned about throwing out irrelevant egomaniacal chaff whenever you're feeling insecure about your mathematical inabilities in your "advanced" courses. how french, how academic!
