Jim Gillogly wrote:
Ray Arachelian wrote:
"Igor Chudov @ home" wrote:
Well, take 11, for example, it cannot be repsesented as a sum of different primes. It cannot, pure and simple.
Bullshit: 7+5+(-1)=11. Last I heard, negative numbers weren't excluded from being primes. 7 is different from 5, -1 is different from 7 and from 5.
If this is boiling down to a definition of primes, I'll haul out my Hardy & Wright, page 2:
A number p is said to be prime if (i) p > 1, (ii) p has no positive divisors except 1 and p. ... It is important to observe that 1 is not reckoned as a prime.
My number theory class at college (admittedly that was three decades ago) also started the prime series at 2 and went up from there. The term "odd primes" always meant 3 and above, not 1 and above.
Well, I suppose negative numbers can't be included because 1 can't be included: 1*1*1*1=1 and the idea is that a prime can only have itself and 1 as factors, where 1 can be factored by itself over and over to an infinite number of 1's, and by that definition you can exclude -1 since -1=(-1*1*-1*1), and so if we take -5 and factor it to -5 and 1 it's good, but it can also be factored to -1 and 5. IMHO 1 and -1 being shunned in this way is a bit silly, but whatever... :^) (Same applies to zero since 0=0*0*0*0*0, but zero has the built in difference of that it can't be divided by itself at all.) So I guess I have to take back 7+5+(-1) and go with Jim's 1+3+7, but fuck, that won't work either since 1 isn't a prime... So I guess Igor is right on this one. Sorry Jim... Any other ideas on 11? =====================================Kaos=Keraunos=Kybernetos============== .+.^.+.| Sunder |Prying open my 3rd eye. So good to see |./|\. ..\|/..|sunder@sundernet.com|you once again. I thought you were |/\|/\ <--*-->| ------------------ |hiding, and you thought that I had run |\/|\/ ../|\..| "A toast to Odin, |away chasing the tail of dogma. I opened|.\|/. .+.v.+.|God of screwdrivers"|my eye and there we were.... |..... ======================= http://www.sundernet.com ==========================