RE: Goldbach's Conjecture (fwd)
Forwarded message:
Date: Fri, 20 Nov 1998 09:41:01 -0600 From: Mark Hahn <mhahn@tcbtech.com> Subject: RE: Goldbach's Conjecture (fwd)
At 09:39 PM 11/19/98 -0600, Jim Choate instructed:
It's interesting that Fermat doesn't mention that the only prime that can use two as a factor is 4. And you can't factor 2 at all since we eliminate 1 as a potential candidate (another issue of symmetry breaking simply so we don't have to write '....works for every prime but 1' on all our theorems).
I thought I was following along until I got here, and got very lost. First question: I think the first sentence implies 4 is prime, so I must have the emphasis wrong.
No, I made a typo. I got so focused on primes last nite that I seem to have typed it in instead of 'even'. I didn't notice it when I saw it posted to the list. My mistake, sorry for the confusion. What started this whole enquiry for me was the realization that the multiplication identity axiom is related to the definition of a prime. Then add on top of that the reason we exclude 1 is so we don't have to write '...except for the prime 1' on the end of lots of number theory (re Richard Feynman's comment during the Challenger Investigation). It was the realization that if we go ahead and include 1 so the axioms are in line with each other (and use our cut&paste feature for the '...1...') then perhaps it would provide a more consistent base and just maybe some of the extant problems in number theory might become solvable in other ways. My original intention was to get a copy of Doug Lenat's EURISKO theorem proving program and change the definition of prime in its database and note the results (after converting it to Perl from LISP). What started all that is that I'm slowly going through 'An Introduction to Algebraic Structures' by J. Landin (Dover) creating a cheat-sheet of number theory that eventualy I hope to post on my webpage for reference. ____________________________________________________________________ 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 --'- --------------------------------------------------------------------
Jim Choate wrote:
What started this whole enquiry for me was the realization that the multiplication identity axiom is related to the definition of a prime. Then add on top of that the reason we exclude 1 is so we don't have to write '...except for the prime 1' on the end of lots of number theory (re Richard Feynman's comment during the Challenger Investigation). It was the realization that if we go ahead and include 1 so the axioms are in line with each other (and use our cut&paste feature for the '...1...') then perhaps it would provide a more consistent base and just maybe some of the extant problems in number theory might become solvable in other ways. My original intention was to get a copy of Doug Lenat's EURISKO theorem proving program and change the definition of prime in its database and note the results (after converting it to Perl from LISP). What started all that is that I'm slowly going through 'An Introduction to Algebraic Structures' by J. Landin (Dover) creating a cheat-sheet of number theory that eventualy I hope to post on my webpage for reference.
If you 'define' 1 to be 'prime', you are 'defining' Goldbach's conjecture 'away'! M. K. Shen
A group is only as useful as the special and similar properties items in the group share. Primes are no exception. One isn't included in the set of primes because it has special properties beyond or inconsistent with the properties of primes. As to the notion that implementing your brilliant idea "would [perhaps] provide a more consistent base and just maybe some of the extant problems in number theory might become solvable in other ways", all I can say is Puhleez... In Gauss, Fermat, Wiles, et al versus Jim Choate, I'd put my money on the former. Sorry for the rude response, I just don't like being sent hostile messages to my personal email account. Blake Buzzini, PSU -----Original Message----- From: owner-cypherpunks@Algebra.COM [mailto:owner-cypherpunks@Algebra.COM] On Behalf Of Jim Choate Sent: Friday, November 20, 1998 10:16 AM To: Cypherpunks Distributed Remailer Subject: RE: Goldbach's Conjecture (fwd) Forwarded message:
Date: Fri, 20 Nov 1998 09:41:01 -0600 From: Mark Hahn <mhahn@tcbtech.com> Subject: RE: Goldbach's Conjecture (fwd)
It's interesting that Fermat doesn't mention that the only prime that can use two as a factor is 4. And you can't factor 2 at all since we eliminate 1 as a potential candidate (another issue of symmetry breaking simply so we don't have to write '....works for every prime but 1' on all our
At 09:39 PM 11/19/98 -0600, Jim Choate instructed: theorems).
I thought I was following along until I got here, and got very lost. First question: I think the first sentence implies 4 is prime, so I must have the emphasis wrong.
No, I made a typo. I got so focused on primes last nite that I seem to have typed it in instead of 'even'. I didn't notice it when I saw it posted to the list. My mistake, sorry for the confusion. What started this whole enquiry for me was the realization that the multiplication identity axiom is related to the definition of a prime. Then add on top of that the reason we exclude 1 is so we don't have to write '...except for the prime 1' on the end of lots of number theory (re Richard Feynman's comment during the Challenger Investigation). It was the realization that if we go ahead and include 1 so the axioms are in line with each other (and use our cut&paste feature for the '...1...') then perhaps it would provide a more consistent base and just maybe some of the extant problems in number theory might become solvable in other ways. My original intention was to get a copy of Doug Lenat's EURISKO theorem proving program and change the definition of prime in its database and note the results (after converting it to Perl from LISP). What started all that is that I'm slowly going through 'An Introduction to Algebraic Structures' by J. Landin (Dover) creating a cheat-sheet of number theory that eventualy I hope to post on my webpage for reference. ____________________________________________________________________ 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 --'- --------------------------------------------------------------------
participants (3)
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Blake Buzzini -
Jim Choate -
Mok-Kong Shen