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