On Jul 7, 10:17 pm, amor...@xenon.Stanford.EDU (Alan Morgan) wrote: > In article <01ecf301-15ba-4bfb-83c3-f4e8e18c9...@o18g2000pra.googlegroups.com>, > Constructive Truth <scribe...@aol.com> wrote: > > >I am afraid, necessarily you misunderstand the direct language of my > >claim. > > >My claim is: > > >1. every prime is of the form 2N+1. > > Not only is your statement trivial and completely uninteresting (every > prime number is odd. Really? Could that be because even numbers are, > by definition, divisible by 2, and thus not prime?), it isn't even > completely correct. 2 is a prime, but is not of the form 2N+1. > > So your claim is both trivial and false. Have no fear! One minor > change: > > Musatov-Morgan Theorem > Every prime > 2 is of the form 2N+1 > > and it's now trivial and true. What's next? A variation on the > Goldbach Conjecture where you hypothesize that every number > 2 > can be written as the sum of two other numbers? > > Alan > -- > Defendit numerus
Thank you for your feedback and write up. Very cool!
Can you explain something to me please? By your comments, I understand, 2 N + 1 = odd. But what else can we say about 2 N + 1 ?
Here are a list of statements, I would like to know if we can properly decide from 2 N + 1:
(All of the below statements assume P > 2, as you asserted.)
Can we say....? (If every prime > 2 is 2 N + 1 = odd)
1. 2 N + 1 = P an (odd) prime 1/2 (of an even) 2P?
2. Can we then write for every prime > 2:
2 N + 1 = P (odd) and 2P (Even), N is also always even?
3. Can the above statement equivocally be stated:
2 (even N) + 1 = Every Prime = 1/2 2P or 1/2 * 4 (even N + 2)?
2 * 8 + 1 = 17 (a prime) = 1/2 (17*2) or 1/2 * (4 * 8 + 2)?
Thank you for your time an patience.
> Musatov-Morgan Theorem > Every prime > 2 is of the form 2N+1