mike
Posts:
34
Registered:
10/29/08


Re: Musatov Prime Generalization Conjecture
Posted:
Jul 12, 2009 10:59 PM


In article <00e966454c61491b8a792a1ae4d3cf60 @d4g2000yqa.googlegroups.com>, scriber17@aol.com says... > On Jul 8, 7:01 pm, mike <m....@irl.cri.replacethiswithnz> wrote: > > In article <88f7a7fc702c47ac8f3e66088faf4487 > > @z4g2000prh.googlegroups.com>, marty.musa...@gmail.com says... > > > > > > > > > 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? > > > > I assume that you trying to state: > > > > For all primes P of the form P = 2*N + 1, the number 2*P is even. > > > > If so then it is trivially true by definition. > > > > > > > > > 2. Can we then write for every prime > 2: > > > > > 2 N + 1 = P (odd) and 2P (Even), N is also always > > > even? > > > > Here you appear to be stating: > > For all P > 2, P = 4*N + 1, for some natural number N. > > > > If so then this is trivially false as it doesn't hold true for 7. > > > > > > > > > 3. Can the above statement equivocally be stated: > > > > > 2 (even N) + 1 = Every Prime > 2 = 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 ? > > > > This seems teh same as 2 above. If so then it is false. > > > > Marty, it may interest you to note that as well as: > > > > For all P > 2, P = 2*N + 1 > > > > being true, it is also the case that: > > > > For all P > 3, P = 6*N +/ 1 > > > >  Mike > > This is very interesting. Thanks Mike. So we have all primes > 2 may > be written as 2 N + 1 or 6 N + /  1. Can these equations be combined > to deduce something further? > Oh yes, there are lots more patterns! How about: For all P > 5, P = 30*N +/ {1,7,11,13}
...with the obvious interpretation of the {} brackets.
Mike

