Re: Goldbach's Conjecture - a question about prime sums of odd numbers (fwd)
Forwarded message:
Date: Thu, 19 Nov 1998 12:18:26 -0500 From: Ray Arachelian <sunder@brainlink.com> Subject: Re: Goldbach's Conjecture - a question about prime sums of odd numbers
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...
A prime is defined as *ANY* number (note the definition doesn't mention sign or magnitude nor does it exclude any numbers a priori) that has no multiplicative factors other than itself and 1. 1 * 1 = 1 so it is clearly prime. Now, if a particular branch of number theory wants to extend it and make it only numbers >=2 that is fine, I'm not working in that branch anyway. ____________________________________________________________________ Lawyers ask the wrong questions when they don't want the right answers. Scully (X-Files) The Armadillo Group ,::////;::-. James Choate Austin, Tx /:'///// ``::>/|/ ravage@ssz.com www.ssz.com .', |||| `/( e\ 512-451-7087 -====~~mm-'`-```-mm --'- --------------------------------------------------------------------
Ray Arachelian wrote:
Actually the issue is 1=1*1, 1=1*1*1 ... 1=1^n. If 1 is prime, then -1 must be prime since -1=1^n where n is odd and 1=1^n where any n is used. The fact that 1 can be factored from itself recursively is the issue.
Duh! I must not have had enough caffeine this morning. Above should say -1=-1^n where N is odd. -- =====================================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 ==========================
Jim Choate wrote:
Forwarded message:
Date: Thu, 19 Nov 1998 12:18:26 -0500 From: Ray Arachelian <sunder@brainlink.com> Subject: Re: Goldbach's Conjecture - a question about prime sums of odd numbers
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...
A prime is defined as *ANY* number (note the definition doesn't mention sign or magnitude nor does it exclude any numbers a priori) that has no multiplicative factors other than itself and 1.
1 * 1 = 1 so it is clearly prime.
Now, if a particular branch of number theory wants to extend it and make it only numbers >=2 that is fine, I'm not working in that branch anyway.
Actually the issue is 1=1*1, 1=1*1*1 ... 1=1^n. If 1 is prime, then -1 must be prime since -1=1^n where n is odd and 1=1^n where any n is used. The fact that 1 can be factored from itself recursively is the issue. (If the above weren't true, then -1 could be prime without affecting whether -3's lack of primality: -3=-1*3 and -3=1*-3.) (See: http://forum.swarthmore.edu/dr.math/problems/1isprime.html ) -- =====================================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 ==========================
Ray Arachelian wrote:
Jim Choate wrote:
Forwarded message:
Date: Thu, 19 Nov 1998 12:18:26 -0500 From: Ray Arachelian <sunder@brainlink.com> Subject: Re: Goldbach's Conjecture - a question about prime sums of odd numbers
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...
A prime is defined as *ANY* number (note the definition doesn't mention sign or magnitude nor does it exclude any numbers a priori) that has no multiplicative factors other than itself and 1.
1 * 1 = 1 so it is clearly prime.
Now, if a particular branch of number theory wants to extend it and make it only numbers >=2 that is fine, I'm not working in that branch anyway.
Actually the issue is 1=1*1, 1=1*1*1 ... 1=1^n. If 1 is prime, then -1 must be prime since -1=1^n where n is odd and 1=1^n where any n is used. The fact that 1 can be factored from itself recursively is the issue.
People, please open ANY math book and see the definition for yourselves. 1 is not a prime by definition. Not because of any other reason. Besides, -1=1^n is just not true for any n. igor
(If the above weren't true, then -1 could be prime without affecting whether -3's lack of primality: -3=-1*3 and -3=1*-3.)
(See: http://forum.swarthmore.edu/dr.math/problems/1isprime.html )
--
=====================================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 ==========================
- Igor.
participants (3)
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ichudov＠Algebra.COM -
Jim Choate -
Ray Arachelian